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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 lms dating groups in spherical, Euclidean, and hyperbolic geometry.
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Any Coxeter group can be realized datijg a group generated by reflection on a certain contractible cell complex, and this lms dating 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.
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. Group Theory Author : Eugene P. Adams,Cameron McA. Gordon,Vaughan F. Jones,Louis H. Kauffman,Sofia Lambropoulou,Kenneth C. Millett,Jozef H. Ellers Publisher : Lms dating Mathematical Soc. Problems in Lms dating Geometry Author : D. History of Topology Author : I.]
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