2018 Fiscal Year Final Research Report
Remodelling Kleinin group theory using ergodic theory and complex analysis
| Project/Area Number |
16K13756
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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 | Osaka University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
角 大輝 大阪大学, 理学研究科, 准教授 (40313324)
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| Research Collaborator |
Miyachi Hideki
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | Klein群 / Teichmuller空間 / 擬等角写像 |
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| Outline of Final Research Achievements |
We remodelled Kleinian group theory and notions appearing there, which was expressed only in terms of three-dimensional topology before, to a form which can be described in terms of complex analysis, in joint work with a Korean mathematician Woojin Jeon among others. Furthermore in collaboration with Papadopoulos at Strasbourg, we showed that the mapping class group actions on measured lamination space equipped with intersection form or geodesic lamination space with left-Hausdorff topology have rigidity. Collborating with applied mathematicians in Gottingen, we gave a numeral index for finger prints making use of quasi-conformal maps and holomorphic quadratic differentials.
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| Free Research Field |
位相幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
Klein群の理論を3次元位相幾何学に依存しない形に拡張していくことにより，より開かれた理論体系とすることができた．これにより，この理論が，幾何的群論，Teichmuller空間論，複素力学系など数学内部で応用できるようになったのみならず，指紋の数値化という応用数学の結果にも結びつけることができた．
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