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Groups of Exceptional Type, Coxeter Groups and Related Geometries

2014-04-02 Mathematics
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Release : 2014-04-02
Genre : Mathematics
Kind : eBook
Book Rating : 140/5 ( reviews)

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Book Synopsis Groups of Exceptional Type, Coxeter Groups and Related Geometries by : N.S. Narasimha Sastry

Download or read book Groups of Exceptional Type, Coxeter Groups and Related Geometries written by N.S. Narasimha Sastry. This book was released on 2014-04-02. Available in PDF, EPUB and Kindle. Book excerpt: 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 Geometry and Topology of Coxeter Groups

2008 Mathematics
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Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 384/5 ( reviews)

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Book Synopsis The Geometry and Topology of Coxeter Groups by : Michael Davis

Download or read book The Geometry and Topology of Coxeter Groups written by Michael Davis. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Reflection Groups and Coxeter Groups

1992-10 Mathematics
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Release : 1992-10
Genre : Mathematics
Kind : eBook
Book Rating : 137/5 ( reviews)

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Book Synopsis Reflection Groups and Coxeter Groups by : James E. Humphreys

Download or read book Reflection Groups and Coxeter Groups written by James E. Humphreys. This book was released on 1992-10. Available in PDF, EPUB and Kindle. Book excerpt: This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.

Combinatorics of Coxeter Groups

2006-02-25 Mathematics
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Release : 2006-02-25
Genre : Mathematics
Kind : eBook
Book Rating : 967/5 ( reviews)

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Book Synopsis Combinatorics of Coxeter Groups by : Anders Bjorner

Download or read book Combinatorics of Coxeter Groups written by Anders Bjorner. This book was released on 2006-02-25. Available in PDF, EPUB and Kindle. Book excerpt: 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

Groups of Lie Type and Their Geometries

1995 Electronic books
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Release : 1995
Genre : Electronic books
Kind : eBook
Book Rating : 005/5 ( reviews)

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Book Synopsis Groups of Lie Type and Their Geometries by : William M. Kantor

Download or read book Groups of Lie Type and Their Geometries written by William M. Kantor. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: Presented here are papers from the 1993 Como meeting on groups of Lie type and their geometries.

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