Combinatorics 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 Combinatorics of Coxeter Groups write by Anders Bjorner. This book was released on 2006-02-25. Combinatorics of Coxeter Groups available 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
Combinatorics of Coxeter Groups
Combinatorics 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 Combinatorics of Coxeter Groups write by Anders Bjorner. This book was released on 2005-05-31. Combinatorics of Coxeter Groups available 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
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups
Generalized Noncrossing Partitions and Combinatorics 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 Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups write by Drew Armstrong. This book was released on 2009-10-08. Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups available in PDF, EPUB and Kindle. This memoir is a refinement of the author's PhD thesis -- written at Cornell University (2006). It is primarily a desription of new research but also includes a substantial amount of background material. At the heart of the memoir the author introduces and studies a poset $NC^{(k)}(W)$ for each finite Coxeter group $W$ and each positive integer $k$. When $k=1$, his definition coincides with the generalized noncrossing partitions introduced by Brady and Watt in $K(\pi, 1)$'s for Artin groups of finite type and Bessis in The dual braid monoid. When $W$ is the symmetric group, the author obtains the poset of classical $k$-divisible noncrossing partitions, first studied by Edelman in Chain enumeration and non-crossing partitions.
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.
The Geometry and Topology of Coxeter Groups
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.
