2017 Fiscal Year Final Research Report
Study on the representation of Teichmuller modular groups as a group of rational transformations
| Project/Area Number |
15K04927
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Shimane University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
NAKAMURA GOU 愛知工業大学, 工学部, 准教授 (50319208)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | タイヒミュラー空間 / 写像類群 / リーマン面 / 双曲幾何学 / 不連続群論 |
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| Outline of Final Research Achievements |
We studied parametrizations of the Teichmuller space of a surface of type (g,n). The Teichmuller space, which is a deformation space of hyperbolic structures on the surface, can be parametrized grobally by lengths of d=6g-5+n closed geodesic curves, as already shown by P. Schmutz and others. Our main result is as follows: there exist d closed curves on the surface such that in the variables defined by their lengths the mapping class group acting on the Teichmuller space is represented by a group of rational transformations. As an application of this result, we could find presentations by Humphries generators of all finite subgroups of the mapping class group of closed surface of genus two.
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| Free Research Field |
複素解析学
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