Milnor Fiber Boundary of a Non-isolated Surface Singularity

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Publisher : Springer
ISBN 13 : 3642236472
Total Pages : 241 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Milnor Fiber Boundary of a Non-isolated Surface Singularity by : András Némethi

Download or read book Milnor Fiber Boundary of a Non-isolated Surface Singularity written by András Némethi and published by Springer. This book was released on 2012-01-05 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized.

Milnor Fiber Boundary of a Non-isolated Surface Singularity

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3642236464
Total Pages : 241 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Milnor Fiber Boundary of a Non-isolated Surface Singularity by : András Némethi

Download or read book Milnor Fiber Boundary of a Non-isolated Surface Singularity written by András Némethi and published by Springer Science & Business Media. This book was released on 2012-01-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized.

Singularities and Their Interaction with Geometry and Low Dimensional Topology

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Publisher : Springer Nature
ISBN 13 : 3030619583
Total Pages : 332 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Singularities and Their Interaction with Geometry and Low Dimensional Topology by : Javier Fernández de Bobadilla

Download or read book Singularities and Their Interaction with Geometry and Low Dimensional Topology written by Javier Fernández de Bobadilla and published by Springer Nature. This book was released on 2021-05-27 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.

Singularity Theory

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Publisher : World Scientific
ISBN 13 : 9812707492
Total Pages : 1083 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Singularity Theory by : Denis Cheniot

Download or read book Singularity Theory written by Denis Cheniot and published by World Scientific. This book was released on 2007 with total page 1083 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory. The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.

Singularity Theory

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Publisher :
ISBN 13 : 9814476390
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Singularity Theory by :

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

Normal Surface Singularities

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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.

When Form Becomes Substance

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Publisher : Springer Nature
ISBN 13 : 3030831256
Total Pages : 607 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis When Form Becomes Substance by : Luciano Boi

Download or read book When Form Becomes Substance written by Luciano Boi and published by Springer Nature. This book was released on 2022-11-30 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interdisciplinary volume collects contributions from experts in their respective fields with as common theme diagrams. Diagrams play a fundamental role in the mathematical visualization and philosophical analysis of forms in space. Some of the most interesting and profound recent developments in contemporary sciences, whether in topology, geometry, dynamic systems theory, quantum field theory or string theory, have been made possible by the introduction of new types of diagrams, which, in addition to their essential role in the discovery of new classes of spaces and phenomena, have contributed to enriching and clarifying the meaning of the operations, structures and properties that are at the heart of these spaces and phenomena. The volume gives a closer look at the scope and the nature of diagrams as constituents of mathematical and physical thought, their function in contemporary artistic work, and appraise, in particular, the actual importance of the diagrams of knots, of braids, of fields, of interaction, of strings in topology and geometry, in quantum physics and in cosmology, but also in theory of perception, in plastic arts and in philosophy. The editors carefully curated this volume to be an inspiration to students and researchers in philosophy, phenomenology, mathematics and the sciences, as well as artists, musicians and the general interested audience.

Handbook of Geometry and Topology of Singularities II

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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.

4-Manifolds and Kirby Calculus

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Publisher : American Mathematical Society
ISBN 13 : 1470474557
Total Pages : 576 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis 4-Manifolds and Kirby Calculus by : Robert E. Gompf

Download or read book 4-Manifolds and Kirby Calculus written by Robert E. Gompf and published by American Mathematical Society. This book was released on 2023-08-10 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the early 1980s, there has been an explosive growth in 4-manifold theory, particularly due to the influx of interest and ideas from gauge theory and algebraic geometry. This book offers an exposition of the subject from the topological point of view. It bridges the gap to other disciplines and presents classical but important topological techniques that have not previously appeared in the literature. Part I of the text presents the basics of the theory at the second-year graduate level and offers an overview of current research. Part II is devoted to an exposition of Kirby calculus, or handlebody theory on 4-manifolds. It is both elementary and comprehensive. Part III offers in-depth treatments of a broad range of topics from current 4-manifold research. Topics include branched coverings and the geography of complex surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces. The authors present many important applications. The text is supplemented with over 300 illustrations and numerous exercises, with solutions given in the book. I greatly recommend this wonderful book to any researcher in 4-manifold topology for the novel ideas, techniques, constructions, and computations on the topic, presented in a very fascinating way. I think really that every student, mathematician, and researcher interested in 4-manifold topology, should own a copy of this beautiful book. —Zentralblatt MATH This book gives an excellent introduction into the theory of 4-manifolds and can be strongly recommended to beginners in this field … carefully and clearly written; the authors have evidently paid great attention to the presentation of the material … contains many really pretty and interesting examples and a great number of exercises; the final chapter is then devoted to solutions of some of these … this type of presentation makes the subject more attractive and its study easier. —European Mathematical Society Newsletter

Singularities of Mappings

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Publisher : Springer Nature
ISBN 13 : 3030344401
Total Pages : 567 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Singularities of Mappings by : David Mond

Download or read book Singularities of Mappings written by David Mond and published by Springer Nature. This book was released on 2020-01-23 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings. Part I of the book develops the now classical real C∞ and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic. By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material, make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.

Singular Points of Complex Hypersurfaces. (AM-61), Volume 61

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Publisher : Princeton University Press
ISBN 13 : 1400881811
Total Pages : 130 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Singular Points of Complex Hypersurfaces. (AM-61), Volume 61 by : John Milnor

Download or read book Singular Points of Complex Hypersurfaces. (AM-61), Volume 61 written by John Milnor and published by Princeton University Press. This book was released on 2016-03-02 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Singular Points of Complex Hypersurfaces. (AM-61), Volume 61, will be forthcoming.

Introduction to Singularities and Deformations

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Publisher : Springer Science & Business Media
ISBN 13 : 3540284192
Total Pages : 482 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 482 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.

An Introduction to Contact Topology

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Publisher : Cambridge University Press
ISBN 13 : 1139467956
Total Pages : 8 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis An Introduction to Contact Topology by : Hansjörg Geiges

Download or read book An Introduction to Contact Topology written by Hansjörg Geiges and published by Cambridge University Press. This book was released on 2008-03-13 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.

Foliations and the Geometry of 3-Manifolds

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Publisher : Oxford University Press on Demand
ISBN 13 : 0198570082
Total Pages : 378 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Foliations and the Geometry of 3-Manifolds by : Danny Calegari

Download or read book Foliations and the Geometry of 3-Manifolds written by Danny Calegari and published by Oxford University Press on Demand. This book was released on 2007-05-17 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.

Holomorphic Curves in Low Dimensions

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Publisher : Springer
ISBN 13 : 3319913719
Total Pages : 294 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Holomorphic Curves in Low Dimensions by : Chris Wendl

Download or read book Holomorphic Curves in Low Dimensions written by Chris Wendl and published by Springer. This book was released on 2018-06-28 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019

From Stein to Weinstein and Back

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Publisher : American Mathematical Soc.
ISBN 13 : 0821885332
Total Pages : 379 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis From Stein to Weinstein and Back by : Kai Cieliebak

Download or read book From Stein to Weinstein and Back written by Kai Cieliebak and published by American Mathematical Soc.. This book was released on 2012 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the interplay between complex and symplectic geometry in affine complex manifolds. Affine complex (a.k.a. Stein) manifolds have canonically built into them symplectic geometry which is responsible for many phenomena in complex geometry and analysis. The goal of the book is the exploration of this symplectic geometry (the road from 'Stein to Weinstein') and its applications in the complex geometric world of Stein manifolds (the road 'back').

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 888 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt: