The Geometry and Topology of Coxeter Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Geometry and Topology of Coxeter Groups write by Michael Davis. This book was released on 2008. The Geometry and Topology of Coxeter Groups available 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.
The Geometry and Topology of Coxeter Groups. (LMS-32)
The Geometry and Topology of Coxeter Groups. (LMS-32) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Geometry and Topology of Coxeter Groups. (LMS-32) write by Michael Davis. This book was released on 2012-11-26. The Geometry and Topology of Coxeter Groups. (LMS-32) available 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.
Geometric and Topological Aspects of Coxeter Groups and Buildings
Geometric and Topological Aspects of Coxeter Groups and Buildings - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric and Topological Aspects of Coxeter Groups and Buildings write by Anne Thomas. This book was released on 2018. Geometric and Topological Aspects of Coxeter Groups and Buildings available in PDF, EPUB and Kindle.
Geometric and Topological Aspects of Coxeter Groups and Buildings
Geometric and Topological Aspects of Coxeter Groups and Buildings - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric and Topological Aspects of Coxeter Groups and Buildings write by Anne Thomas. This book was released on 2018. Geometric and Topological Aspects of Coxeter Groups and Buildings available in PDF, EPUB and Kindle. 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.
Reflection Groups and Coxeter Groups
Reflection Groups and Coxeter Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Reflection Groups and Coxeter Groups write by James E. Humphreys. This book was released on 1992-10. Reflection Groups and Coxeter Groups available 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.
