000			02203cam a2200277 a 4500
001			14674784
005			20250611102844.0
008			061218s2008 njua b 001 0 eng
020			_a9780691131382
040			_aCSL _cCSL
041			_2eng _aeng
084			_aB27 P8 NBHM _qCSL
100	1		_aDavis, Michael, _eauthor. _9509726
245	1	4	_aGeometry and topology of coxeter groups
260			_aPrinceton : _bPrinceton University Press, _cc2008.
300			_axiv, 584 p. : _bill. ; _c24 cm.
490	1		_aLondon Mathematical Society monographs
504			_aIncludes bibliographical references (p. [555]-572) and index.
520			_aThe 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.
650		0	_aCoxeter groups. _9812543
650		0	_aTorsor (algebraic geometry). _9812544
650		0	_aGeometric group theory. _9812545
650		0	_aPolytope. _9812546
830		0	_aLondon Mathematical Society monographs. _9812547
942			_2CC _n0 _cTEXL _hB27 P8 NBHM
999			_c1431591 _d1431591