LEADER 04347nam 2200613 450 001 9910788853503321 005 20170822144313.0 010 $a1-4704-0522-9 035 $a(CKB)3360000000465100 035 $a(EBL)3114069 035 $a(SSID)ssj0000889051 035 $a(PQKBManifestationID)11497165 035 $a(PQKBTitleCode)TC0000889051 035 $a(PQKBWorkID)10866179 035 $a(PQKB)10362863 035 $a(MiAaPQ)EBC3114069 035 $a(RPAM)15358357 035 $a(PPN)195418050 035 $a(EXLCZ)993360000000465100 100 $a20080708h20082008 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe mapping class group from the viewpoint of measure equivalence theory /$fYoshikata Kida 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2008] 210 4$dİ2008 215 $a1 online resource (206 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 916 300 $a"November 2008, volume 196, number 916 (third of 5 numbers )." 311 $a0-8218-4196-3 320 $aIncludes bibliographical references (pages 183-186) and index. 327 $a""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Property A for the curve complex""; ""1. Geometry of the curve complex""; ""2. Generalities for property A""; ""3. Property A for the curve complex""; ""4. Exceptional surfaces""; ""Chapter 3. Amenability for the action of the mapping class group on the boundary of the curve complex""; ""1. The mapping class group and the Thurston boundary""; ""2. The boundary at infinity of the curve complex""; ""3. Amenability for the actions of the mapping class group""; ""4. The boundary of the curve complex for an exceptional surface"" 327 $a""Chapter 4. Indecomposability of equivalence relations generated by the mapping class group""""1. Construction of Busemann functions and the MIN set map""; ""2. Preliminaries on discrete measured equivalence relations""; ""3. Reducible elements in the mapping class group""; ""4. Subrelations of the two types: irreducible and amenable ones and reducible ones""; ""5. Canonical reduction systems for reducible subrelations""; ""6. Indecomposability of equivalence relations generated by actions of the mapping class group""; ""7. Comparison with hyperbolic groups"" 327 $a""Chapter 5. Classification of the mapping class groups in terms of measure equivalence I""""1. Reducible subrelations, revisited""; ""2. Irreducible and amenable subsurfaces""; ""3. Amenable, reducible subrelations""; ""4. Classification""; ""Chapter 6. Classification of the mapping class groups in terms of measure equivalence II""; ""1. Geometric lemmas""; ""2. Families of subrelations satisfying the maximal condition""; ""3. Application I (Invariance of complexity under measure equivalence)""; ""4. Application II (The case where complexity is odd)"" 327 $a""5. Application III (The case where complexity is even)""""Appendix A. Amenability of a group action""; ""1. Notation""; ""2. Existence of invariant means""; ""3. The fixed point property""; ""Appendix B. Measurability of the map associating image measures""; ""Appendix C. Exactness of the mapping class group""; ""Appendix D. The cost and l[sup(2)]-Betti numbers of the mapping class group""; ""1. The cost of the mapping class group""; ""2. The l[sup(2)]-Betti numbers of the mapping class group""; ""Appendix E. A group-theoretic argument for Chapter 5""; ""Bibliography""; ""Index""; ""A"" 327 $a""B""""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 916. 606 $aMappings (Mathematics) 606 $aClass groups (Mathematics) 606 $aMeasure theory 615 0$aMappings (Mathematics) 615 0$aClass groups (Mathematics) 615 0$aMeasure theory. 676 $a511.3/26 700 $aKida$b Yoshikata$f1982-$01565970 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788853503321 996 $aThe mapping class group from the viewpoint of measure equivalence theory$93836149 997 $aUNINA