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Combinatorial And Toric Homotopy
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Book Synopsis Combinatorial And Toric Homotopy: Introductory Lectures by : Alastair Darby
Download or read book Combinatorial And Toric Homotopy: Introductory Lectures written by Alastair Darby and published by World Scientific. This book was released on 2017-10-20 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning.The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis-Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics.The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students.
Book Synopsis Combinatorial and Toric Homotopy by : Alastair Darby
Download or read book Combinatorial and Toric Homotopy written by Alastair Darby and published by . This book was released on 2018 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning. The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis-Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics. The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students."--Publisher's website.
Book Synopsis Toric Topology by : Victor M. Buchstaber
Download or read book Toric Topology written by Victor M. Buchstaber and published by American Mathematical Soc.. This book was released on 2015-07-15 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism. This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area.
Download or read book Toric Topology written by Megumi Harada and published by American Mathematical Soc.. This book was released on 2008 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Toric topology is the study of algebraic, differential, symplectic-geometric, combinatorial, and homotopy-theoretic aspects of a particular class of torus actions whose quotients are highly structured. The combinatorial properties of this quotient and the equivariant topology of the original manifold interact in a rich variety of ways, thus illuminating subtle aspects of both the combinatorics and the equivariant topology. Many of the motivations and guiding principles of the fieldare provided by (though not limited to) the theory of toric varieties in algebraic geometry as well as that of symplectic toric manifolds in symplectic geometry.This volume is the proceedings of the International Conference on Toric Topology held in Osaka in May-June 2006. It contains about 25 research and survey articles written by conference speakers, covering many different aspects of, and approaches to, torus actions, such as those mentioned above. Some of the manuscripts are survey articles, intended to give a broad overview of an aspect of the subject; all manuscripts consciously aim to be accessible to a broad reading audience of students andresearchers interested in the interaction of the subjects involved. We hope that this volume serves as an enticing invitation to this emerging field.
Book Synopsis Combinatorial Homotopy and 4-dimensional Complexes by : Hans J. Baues
Download or read book Combinatorial Homotopy and 4-dimensional Complexes written by Hans J. Baues and published by Walter de Gruyter. This book was released on 1991 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: The bulk of the book is devoted to the algebraic theory of quadratic modules and their connections with 4-dimensional complexes, Pontrjagin squares, homotopy groups, the cohomology of categories, and algebraic K-theory. The first three chapters provide the background needed and may serve as an introduction to basic combinatorial homotopy theory. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Combinatorial Foundation of Homology and Homotopy by : Hans-Joachim Baues
Download or read book Combinatorial Foundation of Homology and Homotopy written by Hans-Joachim Baues and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new combinatorial foundation of the two concepts, based on a consideration of deep and classical results of homotopy theory, and an axiomatic characterization of the assumptions under which results in this field hold. Includes numerous explicit examples and applications in various fields of topology and algebra.
Book Synopsis Toric Topology and Polyhedral Products by : Anthony Bahri
Download or read book Toric Topology and Polyhedral Products written by Anthony Bahri and published by Springer Nature. This book was released on with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Two-Dimensional Homotopy and Combinatorial Group Theory by : Cynthia Hog-Angeloni
Download or read book Two-Dimensional Homotopy and Combinatorial Group Theory written by Cynthia Hog-Angeloni and published by . This book was released on 1994 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers the current state of knowledge in the geometric and algebraic aspects of two-dimensional homotopy theory.
Book Synopsis Advances in Two-Dimensional Homotopy and Combinatorial Group Theory by : Wolfgang Metzler
Download or read book Advances in Two-Dimensional Homotopy and Combinatorial Group Theory written by Wolfgang Metzler and published by Cambridge University Press. This book was released on 2018 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Useful for both students and experts.
Download or read book Homotopy Theory written by I. M. James and published by Elsevier. This book was released on 2014-05-09 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy Theory contains all the published mathematical work of J. H. C. Whitehead, written between 1947 and 1955. This volume considers the study of simple homotopy types, particularly the realization of problem for homotopy types. It describes Whitehead's version of homotopy theory in terms of CW-complexes. This book is composed of 21 chapters and begins with an overview of a theorem to Borsuk and the homotopy type of ANR. The subsequent chapters deal with four-dimensional polyhedral, the homotopy type of a special kind of polyhedron, and the combinatorial homotopy I and II. These topics are followed by reviews of other homotopy types, such as group extensions with homotopy operators, cohomology systems, secondary boundary operator, algebraic homotopy, and the G-dual of a semi-exact couple. The last chapters examine the connected complex homotopy types and the second non-vanishing homotopy groups. This book will be of great value to mathematicians.
Book Synopsis Combinatorial Foundation of Homology and Homotopy by : Hans-Joachim Baues
Download or read book Combinatorial Foundation of Homology and Homotopy written by Hans-Joachim Baues and published by . This book was released on 2014-01-15 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Real Homotopy of Configuration Spaces by : Najib Idrissi
Download or read book Real Homotopy of Configuration Spaces written by Najib Idrissi and published by Springer Nature. This book was released on 2022-06-11 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a unified and accessible account of recent developments regarding the real homotopy type of configuration spaces of manifolds. Configuration spaces consist of collections of pairwise distinct points in a given manifold, the study of which is a classical topic in algebraic topology. One of this theory’s most important questions concerns homotopy invariance: if a manifold can be continuously deformed into another one, then can the configuration spaces of the first manifold be continuously deformed into the configuration spaces of the second? This conjecture remains open for simply connected closed manifolds. Here, it is proved in characteristic zero (i.e. restricted to algebrotopological invariants with real coefficients), using ideas from the theory of operads. A generalization to manifolds with boundary is then considered. Based on the work of Campos, Ducoulombier, Lambrechts, Willwacher, and the author, the book covers a vast array of topics, including rational homotopy theory, compactifications, PA forms, propagators, Kontsevich integrals, and graph complexes, and will be of interest to a wide audience.
Book Synopsis Combinatorial Methods in Topology and Algebraic Geometry by : John R. Harper
Download or read book Combinatorial Methods in Topology and Algebraic Geometry written by John R. Harper and published by American Mathematical Soc.. This book was released on 1985 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of the areas where combinatorial methods have proven especially fruitful: topology and combinatorial group theory, knot theory, 3-manifolds, homotopy theory and infinite dimensional topology, and four manifolds and algebraic surfaces.
Book Synopsis Topology, Geometry, and Dynamics: V. A. Rokhlin-Memorial by : Anatoly M. Vershik
Download or read book Topology, Geometry, and Dynamics: V. A. Rokhlin-Memorial written by Anatoly M. Vershik and published by American Mathematical Soc.. This book was released on 2021-08-30 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vladimir Abramovich Rokhlin (8/23/1919–12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory. The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-100, held from August 19–23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia. The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.
Book Synopsis Homotopy Theory of Combinatorial Categories by : Matthew John Thibault
Download or read book Homotopy Theory of Combinatorial Categories written by Matthew John Thibault and published by . This book was released on 2013 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we investigate the homotopy theory of combinatorial categories associated to the study of simplicial complexes. A result of McCord allows one to study the homotopy theory of simplicial complexes by studying T0 Alexandroff spaces, and hence posets. In Chapter 2, we analyze two separate results of Clader and of Hardie and Vermeulen which suggest that towers of posets are a natural category to embed the homotopy category of simplicial complexes. After generalizing and clarifying the results of Clader and of Hardie and Vermeulen, we express homotopy classes of maps of simplicial complexes as morphisms in the homotopy category of towers of posets. The formulation of this result suggests that there may be a model structure on the category of towers of posets which implies our main theorem and in which bifibrant approximation is reasonable. Chapter 3 investigates whether we can study the homotopy category of simplicial sets through a possible model category structure on the category of delta sets. We also study functors between the category of semi-categories and the category of delta sets which parallel Quillen functors between Cat and the category of simplicial sets. Finally, in Chapter 4, we prove that the characteristic number of an odd MMM class of a surface bundle depends only on the smooth cobordism type of the total space. As a corollary to this theorem and a theorem of Looijenga, each odd MMM class is realized as an obstruction to possessing a fibering in which the fiber is a surface of low genus.
Book Synopsis Models And Methods For Quantum Condensation And Fluids by : Weizhu Bao
Download or read book Models And Methods For Quantum Condensation And Fluids written by Weizhu Bao and published by World Scientific. This book was released on 2023-01-04 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Institute for Mathematical Sciences at the National University of Singapore hosted a thematic program on Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications from September 2019 to March 2020. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers. This invaluable volume collects six expanded lecture notes with self-contained tutorials. The coverage includes mathematical models and numerical methods for multidimensional solitons in linear and nonlinear potentials; Bose-Einstein condensation (BEC) with dipole-dipole interaction, higher order interaction and spin-orbit coupling; classical and quantum turbulence; and molecular dynamics process based on the first-principle in quantum chemistry.This volume serves to inspire graduate students and researchers who will embark into original research work in these fields.
Book Synopsis The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles by : Richard Wentworth
Download or read book The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles written by Richard Wentworth and published by World Scientific. This book was released on 2018-06-28 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. There is a recent surge of interest following Ngô Bau Châu's proof of the Fundamental Lemma and the work of Kapustin and Witten on the Geometric Langlands program. The program on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, was held at the Institute for Mathematical Sciences at the National University of Singapore during 2014. It hosted a number of lectures on recent topics of importance related to Higgs bundles, and it is the purpose of this volume to collect these lectures in a form accessible to graduate students and young researchers interested in learning more about this field.
