Geometric structures on surfaces and representations into Lie groups
| Project/Area Number |
19K21023
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| Project/Area Number (Other) |
18H05833 (2018)
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Multi-year Fund (2019)
Single-year Grants (2018) |
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| Review Section |
0201:Algebra, geometry, analysis, applied mathematics,and related fields
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| Research Institution | Osaka University |
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Principal Investigator |
Shinpei Baba 大阪大学, 理学研究科, 准教授 (40822870)
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| Project Period (FY) |
2018-08-24 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 複素射影構造 / Teichmuller space / 双曲幾何学 / リーマン面 / character variety / リーマン面の退化 / 指標多様体 / CP^1-structure / Teichmueller space / Complex hyperbolic space / タイヒミュラー空間 / 写像類群 / 双曲幾何 / Anosov表現 |
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| Outline of Research at the Start |
幾何学構造を考えることは数学的な“形”（正確には多様体）を分類するのに有用であることが知られている。特に２次元、３次元の“形”を分類するのには幾何学構造がやくにたつ。この様に、全ての考えられる“形”を考えることは、実世界のもの形のモデルとして有用である。
本研究では曲面上の幾何学構造変形空間の研究を行う。
曲面はごく基本的な研究対象であり、様々な観点から活発に研究され、興味深い空間である。特に、本研究ではホロノミー表現と呼ばれる、代数的な性質との関連を調べることを目的とする。
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| Outline of Final Research Achievements |
Complex projective structures are a type of geometric structures (locally homogeneous structures) on a surface, and it has been studies from various perspective. In general, it is important to analyze degeneration of geometric structures on a surface or a more general manifold, especially, in order to compactify it associated deformation space. Projective structures has been studied traditionally more from its analytic side, but holonomy representations of projective structures are algebraic objects, and it is fascinating to understand the relations between projective structures and their holonomy representations.
In this research project, I studied degeneration of projective structures when their holonomy converges. Under this setting, it is known that the underlying complex structure also generates. I characterized such degeneration of projective structure under the basic assumption that complex structures are pinched along a single loop.
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| Academic Significance and Societal Importance of the Research Achievements |
幾何学を通して，代数的および解析的両面から結びつけている。
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Report
(4 results)
Research Products
(5 results)
