Categorification of quantum invariants of 3-manifolds
| Project/Area Number |
23740062
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Waseda University |
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Principal Investigator |
ITO Noboru 早稲田大学, 理工学術院, 助教 (10580160)
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| Project Period (FY) |
2011 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2011: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| Keywords | 低次元トポロジー / 量子トポロジー / 結び目 / ３次元多様体 / 量子不変量 / ２重複体 / スペクトル系列 / 量子化 / 量子群 / 国際研究者交流（デンマーク） / 国際研究者交流（アメリカ） |
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| Research Abstract |
This study gave a fundamental theory contributing to attack the famous open problem: "Categorificaiton of quantum invariants of 3-manifolds". The key point to solve the problem is that we consider the possibility to define invariants under two kinds of operations, denoted by K1 and K2. The main three results are as follows. (1) We reveal that K1 corresponds to sliding grades of a known categorification. (2) We obtain the objects that are invariant under K2 by redefining a generalization of known categorification. (3) We gave an explicit description of a geometric operation derived from (2).
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Report
(3 results)
Research Products
(38 results)
