The Isomorphism Problem In Coxeter Groups

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The Isomorphism Problem In Coxeter Groups

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Author : C. Patrick Bahls
language : en
Publisher: World Scientific
Release Date : 2005

The Isomorphism Problem In Coxeter Groups written by C. Patrick Bahls and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

The book is the first to give a comprehensive overview of the techniques and tools currently being used in the study of combinatorial problems in Coxeter groups. It is self-contained, and accessible even to advanced undergraduate students of mathematics.The primary purpose of the book is to highlight approximations to the difficult isomorphism problem in Coxeter groups. A number of theorems relating to this problem are stated and proven. Most of the results addressed here concern conditions which can be seen as varying degrees of uniqueness of representations of Coxeter groups. Throughout the investigation, the readers are introduced to a large number of tools in the theory of Coxeter groups, drawn from dozens of recent articles by prominent researchers in geometric and combinatorial group theory, among other fields. As the central problem of the book may in fact be solved soon, the book aims to go further, providing the readers with many techniques that can be used to answer more general questions. The readers are challenged to practice those techniques by solving exercises, a list of which concludes each chapter.

Groups Of Exceptional Type Coxeter Groups And Related Geometries

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Author : N.S. Narasimha Sastry
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-04-02

Groups Of Exceptional Type Coxeter Groups And Related Geometries written by N.S. Narasimha Sastry and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-02 with Mathematics categories.

The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.

The Coxeter Legacy

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Author : Harold Scott Macdonald Coxeter
language : en
Publisher: American Mathematical Soc.
Release Date :

The Coxeter Legacy written by Harold Scott Macdonald Coxeter 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 with Mathematics categories.

This collection of essays on the legacy of mathematican Donald Coxeter is a mixture of surveys, updates, history, storytelling and personal memories covering both applied and abstract maths. Subjects include: polytopes, Coxeter groups, equivelar polyhedra, Ceva's theorum, and Coxeter and the artists.

The Geometry And Topology Of Coxeter Groups Lms 32

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Author : Michael Davis
language : en
Publisher: Princeton University Press
Release Date : 2012-11-26

The Geometry And Topology Of Coxeter Groups Lms 32 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 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.

Aspects Of Infinite Groups A Festschrift In Honor Of Anthony Gaglione

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Author : Benjamin Fine
language : en
Publisher: World Scientific
Release Date : 2008-10-23

Aspects Of Infinite Groups A Festschrift In Honor Of Anthony Gaglione written by Benjamin Fine and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-23 with Mathematics categories.

This book is a festschrift in honor of Professor Anthony Gaglione's sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.

Groups Korea 1988

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Author : Ann C. Kim
language : en
Publisher: Springer
Release Date : 2006-11-14

Groups Korea 1988 written by Ann C. Kim 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.

These proceedings include selected and refereed original papers; most are research papers, a few are comprehensive survey articles.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2008

Mathematical Reviews 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 Mathematics categories.

Computational And Combinatorial Group Theory And Cryptography

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Author : Benjamin Fine
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Computational And Combinatorial Group Theory And Cryptography written by Benjamin Fine 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 2012 with Computers categories.

This volume contains the proceedings of the AMS Special Session on Computational Algebra, Groups, and Applications, held April 30-May 1, 2011, at the University of Nevada, Las Vegas, Nevada, and the AMS Special Session on the Mathematical Aspects of Cryptography and Cyber Security, held September 10-11, 2011, at Cornell University, Ithaca, New York. Over the past twenty years combinatorial and infinite group theory has been energized by three developments: the emergence of geometric and asymptotic group theory, the development of algebraic geometry over groups leading to the solution of the Tarski problems, and the development of group-based cryptography. These three areas in turn have had an impact on computational algebra and complexity theory. The papers in this volume, both survey and research, exhibit the tremendous vitality that is at the heart of group theory in the beginning of the twenty-first century as well as the diversity of interests in the field.

Combinatorics Of Coxeter Groups

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Author : Anders Bjorner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-25

Combinatorics Of Coxeter Groups written by Anders Bjorner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-25 with Mathematics categories.

Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups

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.