04347nam 2200613 450 991081880170332120170822144313.01-4704-0522-9(CKB)3360000000465100(EBL)3114069(SSID)ssj0000889051(PQKBManifestationID)11497165(PQKBTitleCode)TC0000889051(PQKBWorkID)10866179(PQKB)10362863(MiAaPQ)EBC3114069(RPAM)15358357(PPN)195418050(EXLCZ)99336000000046510020080708h20082008 uy| 0engur|n|---|||||txtccrThe mapping class group from the viewpoint of measure equivalence theory /Yoshikata KidaProvidence, Rhode Island :American Mathematical Society,[2008]©20081 online resource (206 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 916"November 2008, volume 196, number 916 (third of 5 numbers )."0-8218-4196-3 Includes bibliographical references (pages 183-186) and index.""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""""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""""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)""""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""""B""""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""Memoirs of the American Mathematical Society ;no. 916.Mappings (Mathematics)Class groups (Mathematics)Measure theoryMappings (Mathematics)Class groups (Mathematics)Measure theory.511.3/26Kida Yoshikata1982-1612854MiAaPQMiAaPQMiAaPQBOOK9910818801703321The mapping class group from the viewpoint of measure equivalence theory3941853UNINA