2010 Fiscal Year Final Research Report
Analysis of structures of infinite dimensional Teichmuller spaces and complex analytic moduli spaces
| Project/Area Number |
20740072
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Chiba University |
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Principal Investigator |
FUJIKAWA Ege Chiba University, 大学院・理学研究科, 准教授 (80433788)
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| Project Period (FY) |
2008 – 2010
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| Keywords | リーマン面 / タイヒミュラー空間 / モジュライ空間 |
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| Research Abstract |
For research of the infinite dimensional Teichmuller space of an analytically infinite Riemann surface, we consider the asymptotic Teichmuller space which is a quotient space of the Teichmuller space. A quasiconformal mapping class of a Riemann surface acts on the asymptotic Teichmuller space biholomorphically as an asymptotic Teichmuller modular transformation, but it can act trivially, which is different from the case of the Teichmuller space. In this research, we gave a characterization of the asymptotically trivial mapping class group. Furthermore, we proved the fixed point theorem for the asymptotic Teichmuller modular group and gave an answer to the asymptotic version of the Nielsen realization problem.
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