LEADER 04686nam 2200649 a 450 001 9910779339103321 005 20200520144314.0 010 $a1-283-85128-8 010 $a1-4008-4594-7 024 7 $a10.1515/9781400845941 035 $a(CKB)2550000000709100 035 $a(EBL)1062357 035 $a(OCoLC)823283891 035 $a(SSID)ssj0000784888 035 $a(PQKBManifestationID)11438754 035 $a(PQKBTitleCode)TC0000784888 035 $a(PQKBWorkID)10783502 035 $a(PQKB)10303046 035 $a(DE-B1597)447213 035 $a(OCoLC)979742294 035 $a(DE-B1597)9781400845941 035 $a(Au-PeEL)EBL1062357 035 $a(CaPaEBR)ebr10631229 035 $a(CaONFJC)MIL416378 035 $a(MiAaPQ)EBC1062357 035 $a(EXLCZ)992550000000709100 100 $a20061218d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe geometry and topology of coxeter groups$b[electronic resource] /$fMichael W. Davis 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$dc2008 215 $a1 online resource (601 p.) 225 1 $aLondon Mathematical Society monographs series 300 $aDescription based upon print version of record. 311 $a0-691-13138-4 320 $aIncludes bibliographical references (p. [555]-572) and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tChapter One. INTRODUCTION AND PREVIEW -- $tChapter Two. SOME BASIC NOTIONS IN GEOMETRIC GROUP THEORY -- $tChapter Three. COXETER GROUPS -- $tChapter Four. MORE COMBINATORIAL THEORY OF COXETER GROUPS -- $tChapter Five. THE BASIC CONSTRUCTION -- $tChapter Six. GEOMETRIC REFLECTION GROUPS -- $tChapter Seven. THE COMPLEX ? -- $tChapter Eight. THE ALGEBRAIC TOPOLOGY OF U AND OF ? -- $tChapter Nine. THE FUNDAMENTAL GROUP AND THE FUNDAMENTAL GROUP AT INFINITY -- $tChapter Ten. ACTIONS ON MANIFOLDS -- $tChapter Eleven. THE REFLECTION GROUP TRICK -- $tChapter Twelve. ? IS CAT(O): THEOREMS OF GROMOV AND MOUSSONG -- $tChapter Thirteen. RIGIDITY -- $tChapter Fourteen. FREE QUOTIENTS AND SURFACE SUBGROUPS -- $tChapter Fifteen. ANOTHER LOOK AT (CO)HOMOLOGY -- $tChapter Sixteen. THE EULER CHARACTERISTIC -- $tChapter Seventeen. GROWTH SERIES -- $tChapter Eighteen. BUILDINGS -- $tChapter Nineteen. HECKE-VON NEUMANN ALGEBRAS -- $tChapter Twenty. WEIGHTED L2-(CO)HOMOLOGY -- $tAppendix A: CELL COMPLEXES -- $tAppendix B: REGULAR POLYTOPES -- $tAppendix C: THE CLASSIFICATION OF SPHERICAL AND EUCLIDEAN COXETER GROUPS -- $tAppendix D: THE GEOMETRIC REPRESENTATION -- $tAppendix E: COMPLEXES OF GROUPS -- $tAppendix F: HOMOLOGY AND COHOMOLOGY OF GROUPS -- $tAppendix G: ALGEBRAIC TOPOLOGY AT INFINITY -- $tAppendix H: THE NOVIKOV AND BOREL CONJECTURES -- $tAppendix I: NONPOSITIVE CURVATURE -- $tAppendix J: L2-(CO)HOMOLOGY -- $tBibliography -- $tIndex 330 $aThe Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures. 410 0$aLondon Mathematical Society monographs. 606 $aCoxeter groups 606 $aGeometric group theory 615 0$aCoxeter groups. 615 0$aGeometric group theory. 676 $a512/.2 686 $aSK 260$2rvk 700 $aDavis$b Michael$f1949 Apr. 26-$01499782 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910779339103321 996 $aThe geometry and topology of coxeter groups$93726146 997 $aUNINA