Algebraic study on low-dimensional topology
| Project/Area Number |
21540078
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
HABIRO Kazuo 京都大学, 数理解析研究所, 准教授 (80346064)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 位相幾何学 / 3次元多様体 / 絡み目 / 量子不変量 / トポロジー / 多様体 / 埋め込み / 基本群 / 量子基本群 / 量子表現空間 / van Kampen定理 / 2重圏 / 結び目 / 底タングル / 3次元様体 / Jones多項式 / 量子化 / 表現多様体 / 分類空間 / コボルディズム / ホモロジーシリンダー / 曲面 / Kirbyカルキュラス / 色つきJones多項式 |
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| Research Abstract |
We studied on several topics in 3-dimensional topology. Jointly with G. Massuyeau, we completed a survey article on homology cylinders over surfaces. We also studied Kirby calculus for framed links in 3-manifolds, power series expansions of the reduced colored Jones polynomials of knots called the"heads"and"tails", and the quantum fundamental groups and the quantum representation varieties for 3-manifolds.
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Report
(4 results)
Research Products
(40 results)
