The Mapping Class Group from the Viewpoint of Measure Equivalence Theory

By Y. Kida. 2005

98 citations recorded by the source corpus.

Introduction Property A for the curve complex Amenability for the actions of the mapping class group on the boundary of the curve complex Indecomposability of equivalence relations generated by the mapping class group Classification of the mapping class groups in terms of measure equivalence I Classification of the mapping class groups in terms of measure equivalence II Appendix A. Amenability of a group action Appendix B. Measurability of the map associating image measures Appendix C. Exactness of the mapping class group Appendix D. The cost and $\ell^{2}$-Betti numbers of the mapping class group Appendix E. A group-theoretic argument for Chapter 5 Bibliography Index.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2911d25ddca55cb4b0d723f645d47b925f61b66c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. A. Furman
2. Y. Kida
3. Damien Gaboriau
4. K. Fujiwara
5. Gregory C. Bell
6. U. Bader
7. Roman Sauer
8. Adrian Ioana

In Mathematical Physics

1. A. Furman
2. Y. Kida
3. Damien Gaboriau
4. K. Fujiwara
5. Gregory C. Bell
6. U. Bader
7. Roman Sauer
8. Adrian Ioana

Citations in the corpus

• Orbit Equivalence and Measured Group Theory (2010, background): “If Γ is a non-exceptional mapping class group, its ME-class consists only in its virtual isomorphism class [Kid08a].”
• The asymptotic dimension of a curve graph is finite (2005, methodology): “After this paper was written we were informed that Kida [31] has shown that a curve graph has not only property A1 but also property A.”
• Measure equivalence rigidity of the mapping class group (2006, background): “In addition to this classification, his cocycle superrigidity theorem has many applications to various rigidity phenomena of higher rank lattices.”
• Integrable measure equivalence and rigidity of hyperbolic lattices (2010, background): “In [33, 35] Kida proved that mapping class groups are taut.”
• A SURVEY OF MEASURED GROUP THEORY (2009, methodology): “Known examples of groups in Creg ⊂ C include groups admitting ”hyperbolic-like” actions of the following types: (see [87], [83])”