Geometry And Topology Of Aspherical Manifolds
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Geometry And Topology Of Aspherical Manifolds
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Author : Luca F. Di Cerbo
language : en
Publisher: American Mathematical Society
Release Date : 2025-03-31
Geometry And Topology Of Aspherical Manifolds written by Luca F. Di Cerbo and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-31 with Mathematics categories.
This volume contains the proceedings of the AMS Special Session on Singer–Hopf Conjecture in Geometry and Topology, held from March 18–19, 2023, at Georgia Institute of Technology, Atlanta, Georgia. It presents a multidisciplinary point of view on the Singer conjecture, the Hopf conjecture, the study on normalized Betti numbers, and several other intriguing questions on the fundamental group and cohomology of aspherical manifolds. This volume highlights many interesting research directions in the study of aspherical manifolds and covers a large collection of problems and conjectures about $L^2$-invariants of aspherical manifolds. It provides a snapshot of contemporary research in mathematics at the interface of geometry and topology, as well as algebraic geometry. The problems are presented from several distinct points of view, and the articles in this volume suggest possible generalizations and bridge a gap with closely related problems in differential geometry, complex algebraic geometry, and geometric topology. The volume can play a role in focusing the attention of the mathematical community on these fascinating problems which continue to resist the siege of geometers and topologists. It is our hope that this volume will become a valuable resource for early career mathematicians interested in these deep and important questions.
The Geometry And Topology Of Coxeter Groups
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Author : Michael Davis
language : en
Publisher: Princeton University Press
Release Date : 2008
The Geometry And Topology Of Coxeter Groups written by Michael Davis and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.
The Geometry And Topology Of Coxeter Groups Lms 32
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Author : Michael W. Davis
language : en
Publisher: Princeton University Press
Release Date : 2012-11-26
The Geometry And Topology Of Coxeter Groups Lms 32 written by Michael W. Davis and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-26 with Mathematics categories.
The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.
Geometry And Topology
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Author : James C. Alexander
language : en
Publisher: Springer
Release Date : 2006-11-14
Geometry And Topology written by James C. Alexander and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Handbook Of Geometric Topology
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Author : R.B. Sher
language : en
Publisher: Elsevier
Release Date : 2001-12-20
Handbook Of Geometric Topology written by R.B. Sher and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-20 with Mathematics categories.
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.
Variations On A Theme Of Borel
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Author : Shmuel Weinberger
language : en
Publisher: Cambridge University Press
Release Date : 2022-12-08
Variations On A Theme Of Borel written by Shmuel Weinberger and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-08 with Mathematics categories.
In the middle of the last century, after hearing a talk of Mostow on one of his rigidity theorems, Borel conjectured in a letter to Serre a purely topological version of rigidity for aspherical manifolds (i.e. manifolds with contractible universal covers). The Borel conjecture is now one of the central problems of topology with many implications for manifolds that need not be aspherical. Since then, the theory of rigidity has vastly expanded in both precision and scope. This book rethinks the implications of accepting his heuristic as a source of ideas. Doing so leads to many variants of the original conjecture - some true, some false, and some that remain conjectural. The author explores this collection of ideas, following them where they lead whether into rigidity theory in its differential geometric and representation theoretic forms, or geometric group theory, metric geometry, global analysis, algebraic geometry, K-theory, or controlled topology.
Introduction To Infinity Categories
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Author : Markus Land
language : en
Publisher: Springer Nature
Release Date : 2021-04-21
Introduction To Infinity Categories written by Markus Land and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-21 with Mathematics categories.
This textbook is an introduction to the theory of infinity-categories, a tool used in many aspects of modern pure mathematics. It treats the basics of the theory and supplies all the necessary details while leading the reader along a streamlined path from the basic definitions to more advanced results such as the very important adjoint functor theorems. The book is based on lectures given by the author on the topic. While the material itself is well-known to experts, the presentation of the material is, in parts, novel and accessible to non-experts. Exercises complement this textbook that can be used both in a classroom setting at the graduate level and as an introductory text for the interested reader.
Geometry Topology
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Author :
language : en
Publisher:
Release Date : 2008
Geometry Topology written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Geometry categories.
The Algebraic Characterization Of Geometric 4 Manifolds
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Author : J. A. Hillman
language : en
Publisher: Cambridge University Press
Release Date : 1994-02-03
The Algebraic Characterization Of Geometric 4 Manifolds written by J. A. Hillman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-03 with Mathematics categories.
This book describes work on the characterization of closed 4-manifolds in terms of familiar invariants such as Euler characteristic, fundamental group, and Stiefel-Whitney classes. Using techniques from homological group theory, the theory of 3-manifolds and topological surgery, infrasolvmanifolds are characterized up to homeomorphism, and surface bundles are characterized up to simple homotopy equivalence. Non-orientable cases are also considered wherever possible, and in the final chapter the results obtained earlier are applied to 2-knots and complex analytic surfaces.
Geometric Topology
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Author : William Hilal Kazez
language : en
Publisher: American Mathematical Soc.
Release Date : 1996-10-22
Geometric Topology written by William Hilal Kazez and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-22 with Mathematics categories.
This is Part 1 of a two-part volume reflecting the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August. The texts include research and expository articles and problem sets. The conference covered a wide variety of topics in geometric topology. Features: Kirby's problem list, which contains a thorough description of the progress made on each of the problems and includes a very complete bibliography, makes the work useful for specialists and non-specialists who want to learn about the progress made in many areas of topology. This list may serve as a reference work for decades to come. Gabai's problem list, which focuses on foliations and laminations of 3-manifolds, collects for the first time in one paper definitions, results, and problems that may serve as a defining source in the subject area.