Geometry and Topology of Coxeter Groups. (LMS-32)
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A01=Michael W. Davis
Algebraic group
Algebraic K-theory
Algebraic topology
Author_Michael W. Davis
Basis (linear algebra)
Bounded set (topological vector space)
Category of abelian groups
Category=PBG
Category=PBM
Category=PBP
Cayley graph
Characterization (mathematics)
Combinatorial group theory
Commutative ring
Compactification (mathematics)
Connectivity (graph theory)
Convex polytope
Coxeter group
CW complex
Degeneracy (mathematics)
Diagram (category theory)
Dimension (vector space)
Disk (mathematics)
Duality (mathematics)
eq_isMigrated=1
eq_nobargain
Fixed point (mathematics)
Fundamental group
Fundamental polygon
Geometric group theory
Geometrization conjecture
Geometry
Girth (graph theory)
Graph (discrete mathematics)
Graph of groups
Group algebra
Half-space (geometry)
Hecke algebra
Homology (mathematics)
Homology sphere
Homotopy
Homotopy group
Homotopy sphere
Hyperbolic 3-manifold
Hyperbolic manifold
Intersection (set theory)
Isometry group
JSJ decomposition
K-cell (mathematics)
Lie algebra
Mathematical induction
Minor (linear algebra)
Module (mathematics)
Mostow rigidity theorem
Neighbourhood (mathematics)
Parity (mathematics)
Polytope
Projection (mathematics)
Quotient space (topology)
Reflection group
Riemannian manifold
Set (mathematics)
Simplicial complex
Sphere theorem (3-manifolds)
Subgroup
Support (mathematics)
Theorem
Three-dimensional space (mathematics)
Topological manifold
Topological space
Topology
Torsor (algebraic geometry)
Uniformization theorem
Variable (mathematics)
Von Neumann algebra
Word problem (mathematics)
Product details
- ISBN 9780691131382
- Weight: 992g
- Dimensions: 152 x 235mm
- Publication Date: 18 Nov 2007
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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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 Poincare 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.
Michael W. Davis is professor of mathematics at Ohio State University.
