2012 Fiscal Year Final Research Report
Research on discrete groups under measure equivalence
| Project/Area Number |
21684004
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
KIDA Yoshikata 京都大学, 大学院・理学研究科, 准教授 (90451517)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 離散群 / 軌道同型 / 測度同値 |
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| Research Abstract |
We introduced coupling rigidity for a discrete countable group, and solved the problem when the amalgamated free product of two discrete countable groups having rigidity has rigidity. As its consequence, we constructed new groups having rigidity, and showed that those groups satisfy rigidity in a sense of orbit equivalence. We computed the abstract commensurators of the Torelli group, the Johnson kernel and the surface braid group, which are special subgroups of the mapping class group of a surface. In particular, we succeeded in describing any automorphism of those groups.
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