The mapping class group from the viewpoint of measure equivalence theory / / Yoshikata Kida

• Record Nr.: UNINA9910818801703321
• Autore: Kida Yoshikata <1982->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2008]; ©2008
• ISBN: 1-4704-0522-9
• Descrizione fisica: 1 online resource (206 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 916
• Disciplina: 511.3/26
• Soggetti: Mappings (Mathematics); Class groups (Mathematics); Measure theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "November 2008, volume 196, number 916 (third of 5 numbers )."
• Nota di bibliografia: Includes bibliographical references (pages 183-186) and index.
• Nota di contenuto: ""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""