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Infinite Group Actions On Polyhedra


Infinite Group Actions On Polyhedra
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Infinite Group Actions On Polyhedra


Infinite Group Actions On Polyhedra
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Author : Michael W. Davis
language : en
Publisher: Springer Nature
Release Date : 2024-05-15

Infinite Group Actions On Polyhedra written by Michael W. Davis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-15 with Mathematics categories.


In the past fifteen years, the theory of right-angled Artin groups and special cube complexes has emerged as a central topic in geometric group theory. This monograph provides an account of this theory, along with other modern techniques in geometric group theory. Structured around the theme of group actions on contractible polyhedra, this book explores two prominent methods for constructing such actions: utilizing the group of deck transformations of the universal cover of a nonpositively curved polyhedron and leveraging the theory of simple complexes of groups. The book presents various approaches to obtaining cubical examples through CAT(0) cube complexes, including the polyhedral product construction, hyperbolization procedures, and the Sageev construction. Moreover, it offers a unified presentation of important non-cubical examples, such as Coxeter groups, Artin groups, and groups that act on buildings. Designed as a resource for graduate students and researchers specializing in geometric group theory, this book should also be of high interest to mathematicians in related areas, such as 3-manifolds.



Infinite Group Actions On Polyhedra


Infinite Group Actions On Polyhedra
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Author : Michael W. Davis
language : en
Publisher: Springer
Release Date : 2024-02-15

Infinite Group Actions On Polyhedra written by Michael W. Davis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-15 with Mathematics categories.


In the past fifteen years, the theory of right-angled Artin groups and special cube complexes has emerged as a central topic in geometric group theory. This monograph provides an account of this theory, along with other modern techniques in geometric group theory. Structured around the theme of group actions on contractible polyhedra, this book explores two prominent methods for constructing such actions: utilizing the group of deck transformations of the universal cover of a nonpositively curved polyhedron and leveraging the theory of simple complexes of groups. The book presents various approaches to obtaining cubical examples through CAT(0) cube complexes, including the polyhedral product construction, hyperbolization procedures, and the Sageev construction. Moreover, it offers a unified presentation of important non-cubical examples, such as Coxeter groups, Artin groups, and groups that act on buildings. Designed as a resource for graduate students and researchers specializing in geometric group theory, this book should also be of high interest to mathematicians in related areas, such as 3-manifolds.



Dynamics Of Discrete Group Action


Dynamics Of Discrete Group Action
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Author : Boris N. Apanasov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-07-22

Dynamics Of Discrete Group Action written by Boris N. Apanasov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-22 with Mathematics categories.


Provides the first systematic study of geometry and topology of locally symmetric rank one manifolds and dynamics of discrete action of their fundamental groups. In addition to geometry and topology, this study involves several other areas of Mathematics – from algebra of varieties of groups representations and geometric group theory, to geometric analysis including classical questions from function theory.



Geometry Of Group Representations


Geometry Of Group Representations
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Author : William Mark Goldman
language : en
Publisher: American Mathematical Soc.
Release Date : 1988

Geometry Of Group Representations written by William Mark Goldman 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 1988 with Mathematics categories.


Contains papers based on talks delivered at the AMS-IMS-SIAM Summer Research Conference on the Geometry of Group Representations, held at the University of Colorado in Boulder in July 1987. This work offers an understanding of the state of research in the geometry of group representations and their applications.



The Geometry And Topology Of Three Manifolds


The Geometry And Topology Of Three Manifolds
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Author : William P. Thurston
language : en
Publisher: American Mathematical Society
Release Date : 2022-07-19

The Geometry And Topology Of Three Manifolds written by William P. Thurston 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 2022-07-19 with Mathematics categories.


William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume IV contains Thurston's highly influential, though previously unpublished, 1977–78 Princeton Course Notes on the Geometry and Topology of 3-manifolds. It is an indispensable part of the Thurston collection but can also be used on its own as a textbook or for self-study.



Low Dimensional Topology And Kleinian Groups


Low Dimensional Topology And Kleinian Groups
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Author : D. B. A. Epstein
language : en
Publisher: CUP Archive
Release Date : 1986

Low Dimensional Topology And Kleinian Groups written by D. B. A. Epstein and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.


Volume 2 is divided into three parts: the first 'Surfaces' contains an article by Thurston on earthquakes and by Penner on traintracks. The second part is entitled 'Knots and 3-Manifolds' and the final part 'Kleinian Groups'.



Mathematical Impressions


Mathematical Impressions
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Author : A. T. Fomenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1991

Mathematical Impressions written by A. T. Fomenko 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 1991 with Art categories.


Soviet mathematician Fomenko augments his technical books and papers with visual impressions of mathematical concepts, often reminiscent of Escher, and with allusions to Breughel and Durer. Over 80 reproductions, a few in color, are accompanied by the artist's explanation of the mathematical principles being suggested. Annotation copyrighted by Book News, Inc., Portland, OR



Conformal Geometry Of Discrete Groups And Manifolds


Conformal Geometry Of Discrete Groups And Manifolds
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Author : Boris N. Apanasov
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24

Conformal Geometry Of Discrete Groups And Manifolds written by Boris N. Apanasov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.


The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)



Group Actions On Manifolds


Group Actions On Manifolds
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Author : Reinhard Schultz
language : en
Publisher: American Mathematical Soc.
Release Date : 1985

Group Actions On Manifolds written by Reinhard Schultz 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 1985 with Mathematics categories.


Presents an understanding of the sorts of problems one studies in group actions and the methods used to study such problems. This book features articles based upon lectures at the 1983 AMS-IMS-SIAM Joint Summer Research Conference, Group Actions on Manifolds, held at the University of Colorado.



The Geometry And Topology Of Coxeter Groups


The Geometry And Topology Of Coxeter Groups
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Author : Michael W. Davis
language : en
Publisher: Springer Nature
Release Date : 2025-07-30

The Geometry And Topology Of Coxeter Groups written by Michael W. Davis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-30 with Mathematics categories.


This book, now in a revised and extended second edition, offers an in-depth account of Coxeter groups through the perspective of geometric group theory. It examines the connections between Coxeter groups and major open problems in topology related to aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer Conjectures. The book also discusses key 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. In addition, this second edition includes new chapters on Artin groups and their Betti numbers. Written by a leading expert, the book is an authoritative reference on the subject.