Algebraic and category-theoretic study of low-dimensional topology
Project/Area Number |
24540077
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
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Research Institution | Kyoto University |
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) |
2012-04-01 – 2016-03-31
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Project Status |
Completed (Fiscal Year 2015)
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Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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Keywords | 3次元多様体 / Kirby計算 / 量子群 / 圏化 / トレース / 量子不変量 / Hochschild-Mitchellホモロジー / 線形圏 / 2圏 / 巡回ホモロジー / カレント代数 / 絡み目 / 枠付き絡み目 / Kirbyカルキュラス / リボン元 / Borromean手術 / 複体 |
Outline of Final Research Achievements |
I studied several topics on 3-dimensional topology and related algebra. Jointly with T. Widmer, I studied Kirby calculus for null-homotopic framed links and null-homologous framed links in 3-manifolds. Jointly with A. Beliakova, Z. Guliyev, A. D. Lauda, B. Webster and M. Zivkovic, I studied categorified quantum groups, in particular the ribbon element, the traces and the pivotal structure. Jointly with T. Q. T. Le, for each finite dimensional complex simple Lie algebra g, I constructed an invariant of integral homology 3-spheres which unify the quantum g invariants at various roots of unity.
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Report
(5 results)
Research Products
(31 results)
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[Presentation] Trace and categorification2015
Author(s)
Kazuo Habiro
Organizer
Categorification in Algebra, Geometry and Physics (A conference in honor of the 60th birthday of Christian Blanchet)
Place of Presentation
カルジェーズ(フランス)
Year and Date
2015-05-06
Related Report
Int'l Joint Research / Invited
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