Geometry Of Coxeter Groups PDF Download
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Author | : Michael Davis |
Publisher | : Princeton University Press |
Total Pages | : 601 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0691131384 |
Download The Geometry and Topology of Coxeter Groups Book in PDF, ePub and Kindle
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.
Author | : James E. Humphreys |
Publisher | : Cambridge University Press |
Total Pages | : 222 |
Release | : 1992-10 |
Genre | : Mathematics |
ISBN | : 9780521436137 |
Download Reflection Groups and Coxeter Groups Book in PDF, ePub and Kindle
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.
Author | : Michael Davis |
Publisher | : Princeton University Press |
Total Pages | : 600 |
Release | : 2012-11-26 |
Genre | : Mathematics |
ISBN | : 1400845947 |
Download The Geometry and Topology of Coxeter Groups. (LMS-32) Book in PDF, ePub and Kindle
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.
Author | : Anders Bjorner |
Publisher | : Springer Science & Business Media |
Total Pages | : 371 |
Release | : 2006-02-25 |
Genre | : Mathematics |
ISBN | : 3540275967 |
Download Combinatorics of Coxeter Groups Book in PDF, ePub and Kindle
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
Author | : Howard Hiller |
Publisher | : Pitman Publishing |
Total Pages | : 230 |
Release | : 1982 |
Genre | : Mathematics |
ISBN | : |
Download Geometry of Coxeter Groups Book in PDF, ePub and Kindle
Author | : Anne Thomas |
Publisher | : |
Total Pages | : |
Release | : 2018 |
Genre | : |
ISBN | : 9783037191897 |
Download Geometric and Topological Aspects of Coxeter Groups and Buildings Book in PDF, ePub and Kindle
Author | : Siobhan Roberts |
Publisher | : |
Total Pages | : 0 |
Release | : 2007 |
Genre | : Biography & Autobiography |
ISBN | : 9781846680076 |
Download King of Infinite Space Book in PDF, ePub and Kindle
Geometry is far more than just shapes and numbers. It governs much of our lives, from architecture and data-mining technology to aerodynamic car design, life-like characters in animated movies, the molecules of food, even our own body chemistry. This title discusses the groundbreaking work of Donald Coxeter, the greatest geometer of his age.
Author | : Alexandre V. Borovik |
Publisher | : Springer Science & Business Media |
Total Pages | : 172 |
Release | : 2009-11-07 |
Genre | : Mathematics |
ISBN | : 0387790667 |
Download Mirrors and Reflections Book in PDF, ePub and Kindle
This graduate/advanced undergraduate textbook contains a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups. Key features include: many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory; a large number of exercises at various levels of difficulty; some Euclidean geometry is included along with the theory of convex polyhedra; no prerequisites are necessary beyond the basic concepts of linear algebra and group theory; and a good index and bibliography The exposition is directed at advanced undergraduates and first-year graduate students.
Author | : Alexandre V. Borovik |
Publisher | : Springer Science & Business Media |
Total Pages | : 292 |
Release | : 2003-07-11 |
Genre | : Mathematics |
ISBN | : 9780817637644 |
Download Coxeter Matroids Book in PDF, ePub and Kindle
Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.
Author | : Harold Scott Macdonald Coxeter |
Publisher | : American Mathematical Soc. |
Total Pages | : 344 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821887608 |
Download The Coxeter Legacy Book in PDF, ePub and Kindle
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.