Handbook Of Geometry And Topology Of Singularities Iv

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Handbook of Geometry and Topology of Singularities IV

Author : José Luis Cisneros-Molina
Publisher :
ISBN 13 : 9783031319273
Total Pages : 0 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Handbook of Geometry and Topology of Singularities IV by : José Luis Cisneros-Molina

Download or read book Handbook of Geometry and Topology of Singularities IV written by José Luis Cisneros-Molina and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research.This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex.Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Handbook of Geometry and Topology of Singularities I

Author : José Luis Cisneros Molina
Publisher : Springer Nature
ISBN 13 : 3030530612
Total Pages : 616 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Handbook of Geometry and Topology of Singularities I by : José Luis Cisneros Molina

Download or read book Handbook of Geometry and Topology of Singularities I written by José Luis Cisneros Molina and published by Springer Nature. This book was released on 2020-10-24 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Handbook of Geometry and Topology of Singularities IV

Author : José Luis Cisneros-Molina
Publisher : Springer Nature
ISBN 13 : 3031319257
Total Pages : 622 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Handbook of Geometry and Topology of Singularities IV by : José Luis Cisneros-Molina

Download or read book Handbook of Geometry and Topology of Singularities IV written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2023-11-10 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Handbook of Geometry and Topology of Singularities II

Author : José Luis Cisneros-Molina
Publisher : Springer Nature
ISBN 13 : 3030780244
Total Pages : 581 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Handbook of Geometry and Topology of Singularities II by : José Luis Cisneros-Molina

Download or read book Handbook of Geometry and Topology of Singularities II written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2021-11-01 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the Handbook of the Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory and related topics. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Handbook of Geometry and Topology of Singularities VI: Foliations

Author : Felipe Cano
Publisher : Springer
ISBN 13 : 9783031541711
Total Pages : 0 pages
Book Rating : 4.5/5 (417 download)

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Book Synopsis Handbook of Geometry and Topology of Singularities VI: Foliations by : Felipe Cano

Download or read book Handbook of Geometry and Topology of Singularities VI: Foliations written by Felipe Cano and published by Springer. This book was released on 2024-08-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the sixth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. Singularities are ubiquitous in mathematics and science in general, and singularity theory is a crucible where different types of mathematical problems converge, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. This Volume VI goes together with Volume V and focuses on singular holomorphic foliations, which is a multidisciplinary field and a whole area of mathematics in itself. Singular foliations arise, for instance, by considering: The fibers of a smooth map between differentiable manifolds, with singularities at the critical points. The integral lines of a vector field, or the action of a Lie group on a manifold. The singularities are the orbits with special isotropy. The kernel of appropriate 1-forms. The singularities are the zeroes of the form. Open books, which naturally appear in singularity theory, are foliations with singular set the binding. These important examples highlight the deep connections between foliations and singularity theory. This volume consists of nine chapters, authored by world experts, which provide in-depth and reader-friendly introductions to some of the foundational aspects of the theory. These introductions also give insights into important lines of further research. Volume VI ends with an Epilogue by one of the current world leaders in the theory of complex foliations, with plenty of open questions and ideas for further research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Handbook of Geometry and Topology of Singularities V: Foliations

Author : Felipe Cano
Publisher : Springer
ISBN 13 : 9783031524806
Total Pages : 0 pages
Book Rating : 4.5/5 (248 download)

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Book Synopsis Handbook of Geometry and Topology of Singularities V: Foliations by : Felipe Cano

Download or read book Handbook of Geometry and Topology of Singularities V: Foliations written by Felipe Cano and published by Springer. This book was released on 2024-05-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fifth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. Singularities are ubiquitous in mathematics and science in general, and singularity theory is a crucible where different types of mathematical problems converge, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. This Volume V focuses on singular holomorphic foliations, which is a multidisciplinary field and a whole area of mathematics in itself. Singular foliations arise, for instance, by considering: The fibers of a smooth map between differentiable manifolds, with singularities at the critical points. The integral lines of a vector field, or the action of a Lie group on a manifold. The singularities are the orbits with special isotropy. The kernel of appropriate 1-forms. The singularities are the zeros of the form. Open books, which naturally appear in singularity theory as foliations with singular set the binding. These important examples highlight the deep connections between foliations and singularity theory. This volume, like its companion Volume VI, also focused on foliations, consists of nine chapters, authored by world experts, which provide in-depth and reader-friendly introductions to some of the foundational aspects of the theory. These introductions also give insights into important lines of further research. The volume starts with a foreword by one of the current world leaders in the theory of complex foliations. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Handbook of Geometry and Topology of Singularities III

Author : José Luis Cisneros-Molina
Publisher : Springer Nature
ISBN 13 : 3030957608
Total Pages : 822 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Handbook of Geometry and Topology of Singularities III by : José Luis Cisneros-Molina

Download or read book Handbook of Geometry and Topology of Singularities III written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2022-06-06 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski’s equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom–Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Singularities in Geometry and Topology

Author :
Publisher :
ISBN 13 : 9814477044
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Singularities in Geometry and Topology by :

Download or read book Singularities in Geometry and Topology written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Singularities in Geometry, Topology, Foliations and Dynamics

Author : José Luis Cisneros-Molina
Publisher : Birkhäuser
ISBN 13 : 3319393391
Total Pages : 231 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Singularities in Geometry, Topology, Foliations and Dynamics by : José Luis Cisneros-Molina

Download or read book Singularities in Geometry, Topology, Foliations and Dynamics written by José Luis Cisneros-Molina and published by Birkhäuser. This book was released on 2017-02-13 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general. In recent years there have been remarkable developments, both in the theory itself and in its relations with other areas. The contributions in this volume originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in celebration of José Seade’s 60th Birthday. It is intended for researchers and graduate students interested in singularity theory and its impact on other fields.

Singularities and Topology of Hypersurfaces

Author : Alexandru Dimca
Publisher : Springer Science & Business Media
ISBN 13 : 9780387977096
Total Pages : 284 pages
Book Rating : 4.9/5 (77 download)

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Book Synopsis Singularities and Topology of Hypersurfaces by : Alexandru Dimca

Download or read book Singularities and Topology of Hypersurfaces written by Alexandru Dimca and published by Springer Science & Business Media. This book was released on 1992-04-29 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the very beginning, algebraic topology has developed under the influ ence of the problems posed by trying to understand the topological properties of complex algebraic varieties (e.g., the pioneering work by Poincare and Lefschetz). Especially in the work of Lefschetz [Lf2], the idea is made explicit that singularities are important in the study of the topology even in the case of smooth varieties. What is known nowadays about the topology of smooth and singular vari eties is quite impressive. The many existing results may be roughly divided into two classes as follows: (i) very general results or theories, like stratified Morse theory and (mixed) Hodge theory, see, for instance, Goresky-MacPherson [GM], Deligne [Del], and Steenbrink [S6]; and (ii) specific topics of great subtlety and beauty, like the study of the funda mental group of the complement in [p>2 of a singular plane curve initiated by Zariski or Griffiths' theory relating the rational differential forms to the Hodge filtration on the middle cohomology group of a smooth projec tive hypersurface. The aim of this book is precisely to introduce the reader to some topics in this latter class. Most of the results to be discussed, as well as the related notions, are at least two decades old, and specialists use them intensively and freely in their work. Nevertheless, it is impossible to find an adequate intro duction to this subject, which gives a good feeling for its relations with other parts of algebraic geometry and topology.

Singularities and Foliations. Geometry, Topology and Applications

Author : Raimundo Nonato Araújo dos Santos
Publisher : Springer
ISBN 13 : 3319736396
Total Pages : 553 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Singularities and Foliations. Geometry, Topology and Applications by : Raimundo Nonato Araújo dos Santos

Download or read book Singularities and Foliations. Geometry, Topology and Applications written by Raimundo Nonato Araújo dos Santos and published by Springer. This book was released on 2018-03-21 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.

Topology and Geometry of Intersections of Ellipsoids in R^n

Author : Santiago López de Medrano
Publisher : Springer Nature
ISBN 13 : 3031283643
Total Pages : 277 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Topology and Geometry of Intersections of Ellipsoids in R^n by : Santiago López de Medrano

Download or read book Topology and Geometry of Intersections of Ellipsoids in R^n written by Santiago López de Medrano and published by Springer Nature. This book was released on 2023-05-24 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an overview of research in the topology and geometry of intersections of quadrics in $\mathbb{R}^n$, with a focus on intersections of concentric ellipsoids and related spaces. Unifying and organizing material previously spread over many articles, it also contains new results. The first part provides very detailed foundations of a wide-ranging theory that could be useful for future developments. It includes chapters on general intersections of quadrics, operations on them, and intersections of concentric and coaxial quadrics. Moving from the general to the specific, the second part focuses on a topological description of transverse intersections of concentric ellipsoids, including a complete description of the case of three ellipsoids, and of some large families of more than three of them. The third part looks at relations to other areas of mathematics such as dynamical systems, complex geometry, contact and symplectic geometry, and other applications. An appendix gathers some technical items and also gives an account of the origins, motivations and progression of the subject, including historical recollections of the author, who has been central to its development.

Differential Geometry from a Singularity Theory Viewpoint

Author : Shyuichi E. T. Al IZUMIYA
Publisher : World Scientific
ISBN 13 : 9814590452
Total Pages : 383 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Differential Geometry from a Singularity Theory Viewpoint by : Shyuichi E. T. Al IZUMIYA

Download or read book Differential Geometry from a Singularity Theory Viewpoint written by Shyuichi E. T. Al IZUMIYA and published by World Scientific. This book was released on 2015-10-29 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Differential Geometry from a Singularity Theory Viewpoint provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces. The book uses singularity theory to capture some key geometric features of surfaces. It describes the theory of contact and its link with the theory of caustics and wavefronts. It then uses the powerful techniques of these theories to deduce geometric information about surfaces embedded in 3, 4 and 5-dimensional Euclidean spaces. The book also includes recent work of the authors and their collaborators on the geometry of sub-manifolds in Minkowski spaces."--

Singularities in Geometry and Topology

Author : Jean-Paul Brasselet
Publisher : World Scientific
ISBN 13 : 9812700226
Total Pages : 917 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Singularities in Geometry and Topology by : Jean-Paul Brasselet

Download or read book Singularities in Geometry and Topology written by Jean-Paul Brasselet and published by World Scientific. This book was released on 2007 with total page 917 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.

Normal Surface Singularities

Author : András Némethi
Publisher : Springer Nature
ISBN 13 : 3031067533
Total Pages : 732 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Normal Surface Singularities by : András Némethi

Download or read book Normal Surface Singularities written by András Némethi and published by Springer Nature. This book was released on 2022-10-07 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology. In this way, it unites the analytic approach with the more recent topological one, combining their tools and methods. In the first chapters, the book sets out the foundations of the theory of normal surface singularities. This includes a comprehensive presentation of the properties of the link (as an oriented 3-manifold) and of the invariants associated with a resolution, combined with the structure and special properties of the line bundles defined on a resolution. A recurring theme is the comparison of analytic and topological invariants. For example, the Poincaré series of the divisorial filtration is compared to a topological zeta function associated with the resolution graph, and the sheaf cohomologies of the line bundles are compared to the Seiberg–Witten invariants of the link. Equivariant Ehrhart theory is introduced to establish surgery-additivity formulae of these invariants, as well as for the regularization procedures of multivariable series. In addition to recent research, the book also provides expositions of more classical subjects such as the classification of plane and cuspidal curves, Milnor fibrations and smoothing invariants, the local divisor class group, and the Hilbert–Samuel function. It contains a large number of examples of key families of germs: rational, elliptic, weighted homogeneous, superisolated and splice-quotient. It provides concrete computations of the topological invariants of their links (Casson(–Walker) and Seiberg–Witten invariants, Turaev torsion) and of the analytic invariants (geometric genus, Hilbert function of the divisorial filtration, and the analytic semigroup associated with the resolution). The book culminates in a discussion of the topological and analytic lattice cohomologies (as categorifications of the Seiberg–Witten invariant and of the geometric genus respectively) and of the graded roots. Several open problems and conjectures are also formulated. Normal Surface Singularities provides researchers in algebraic and differential geometry, singularity theory, complex analysis, and low-dimensional topology with an invaluable reference on this rich topic, offering a unified presentation of the major results and approaches.

Introduction to Singularities and Deformations

Author : Gert-Martin Greuel
Publisher : Springer Science & Business Media
ISBN 13 : 3540284192
Total Pages : 472 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Introduction to Singularities and Deformations by : Gert-Martin Greuel

Download or read book Introduction to Singularities and Deformations written by Gert-Martin Greuel and published by Springer Science & Business Media. This book was released on 2007-02-23 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.

Handbook of Geometric Topology

Author : R.B. Sher
Publisher : Elsevier
ISBN 13 : 0080532853
Total Pages : 1145 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Geometric Topology by : R.B. Sher

Download or read book Handbook of Geometric Topology written by R.B. Sher and published by Elsevier. This book was released on 2001-12-20 with total page 1145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.