| Project/Area Number |
15K13441
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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 |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
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| Research Collaborator |
Zhang Tanran 蘇州大学
Wang Li-Mei 対外経済貿易大学
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | タイヒミュラー空間 / アフィン構造 / 錐特異性 / 双曲計量 / 特異ユークリッド構造 / 射影構造 / 基本群の表現 / 周期行列 / シストール / リーマン面 / 錐計量 / シュワルツ微分 / フックス群 |
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| Outline of Final Research Achievements |
One can assign N pairs of sides to a polygon with 2N sides in the plane. Pasting each pair of sides by a complex affine map yields a Riemann surface with affine structure. Our purpose was to construct a suitable vector bundle over the Teichmueller space which describes those Riemann surfaces arising from this construction. It turns out that it is equivalent to consider the space of affine representations of the fundamental group of a fixed Riemann surface with punctures. Moreover, if the sides have the same length for each pair in the above construction, one obtains a singular Euclidean structure for the Riemann surface. Therefore, we understand that a moduli space of such objects can be understood as a section of the above vector bundle.
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