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Geometric and Topological Aspects of Coxeter Groups and Buildings

2018 MATHEMATICS
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Release : 2018
Genre : MATHEMATICS
Kind : eBook
Book Rating : 892/5 ( reviews)

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Book Synopsis Geometric and Topological Aspects of Coxeter Groups and Buildings by : Anne Thomas

Download or read book Geometric and Topological Aspects of Coxeter Groups and Buildings written by Anne Thomas. This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt: Coxeter groups are groups generated by reflections, and they appear throughout mathematics. Tits developed the general theory of Coxeter groups in order to develop the theory of buildings. Buildings have interrelated algebraic, combinatorial and geometric structures, and are powerful tools for understanding the groups which act on them. These notes focus on the geometry and topology of Coxeter groups and buildings, especially nonspherical cases. The emphasis is on geometric intuition, and there are many examples and illustrations. Part I describes Coxeter groups and their geometric realisations, particularly the Davis complex, and Part II gives a concise introduction to buildings. This book will be suitable for mathematics graduate students and researchers in geometric group theory, as well as algebra and combinatorics. The assumed background is basic group theory, including group actions, and basic algebraic topology, together with some knowledge of Riemannian geometry.

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.

Geometric and Topological Aspects of Coxeter Groups and Buildings

2018
Download Geometric and Topological Aspects of Coxeter Groups and Buildings PDF Online Free

Author :
Release : 2018
Genre :
Kind : eBook
Book Rating : 897/5 ( reviews)

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Book Synopsis Geometric and Topological Aspects of Coxeter Groups and Buildings by : Anne Thomas

Download or read book Geometric and Topological Aspects of Coxeter Groups and Buildings written by Anne Thomas. This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt:

The Geometry and Topology of Coxeter Groups. (LMS-32)

2012-11-26 Mathematics
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Release : 2012-11-26
Genre : Mathematics
Kind : eBook
Book Rating : 947/5 ( reviews)

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Book Synopsis The Geometry and Topology of Coxeter Groups. (LMS-32) by : Michael Davis

Download or read book The Geometry and Topology of Coxeter Groups. (LMS-32) written by Michael Davis. This book was released on 2012-11-26. 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.

Twin Buildings and Applications to S-Arithmetic Groups

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 703/5 ( reviews)

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Book Synopsis Twin Buildings and Applications to S-Arithmetic Groups by : Peter Abramenko

Download or read book Twin Buildings and Applications to S-Arithmetic Groups written by Peter Abramenko. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: This book is addressed to mathematicians and advanced students interested in buildings, groups and their interplay. Its first part introduces - presupposing good knowledge of ordinary buildings - the theory of twin buildings, discusses its group-theoretic background (twin BN-pairs), investigates geometric aspects of twin buildings and applies them to determine finiteness properties of certain S-arithmetic groups. This application depends on topological properties of some subcomplexes of spherical buildings. The background of this problem, some examples and the complete solution for all "sufficiently large" classical buildings are covered in detail in the second part of the book.

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