New perspective on Riemann surfaces of infinite genus and their deformation spaces
| Project/Area Number |
26610014
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
藤川 英華 千葉大学, 大学院理学研究科, 准教授 (80433788)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 関数論 / トポロジー / Hyperbolic geometry / Teichmuller space / Riemann surface / 国際研究者交流 / 国際情報交換 / 多国籍 |
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| Outline of Final Research Achievements |
On the deformation theory of Riemann surfaces, quasiconformal maps have played an important role. In this project, we succeeded in constructing a counterexample of Sullivan-Thurston’claim for quasiconformal motions. We also give a necessary and sufficient condition for a holomorphic motion of a subset of the Riemann sphere parametrized over a Riemann surface to be extended to a holomorphic motion of the Riemann sphere. The condition is given by the monodromy of the motion. This result is related to quasiconformal maps but it has also a topological aspect, the monodromy.
A new concept of Teichmuller space for Riemann surface with countably many points is considered. The research of those Teichmuller spaces will generalize holomorphic motions to those of subsets of Riemann surfaces. Therefore, it will give new interesting problems to related fields of mathematics.
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Report
(4 results)
Research Products
(17 results)
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[Presentation] Tame qc-motions and the monodromy2016
Author(s)
H. Shiga
Organizer
AMS Spring Eastern Sectional Meeting, Special Session on Teichmuller Theory and Related Topics
Place of Presentation
State University of New York at Stony Brook, Stony Brook, NY, USA
Year and Date
2016-03-20
Related Report
Int'l Joint Research / Invited
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