Studies on derived string topology developed on Gorenstein spaces
| Project/Area Number |
25287008
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Shinshu University |
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Principal Investigator |
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| Research Collaborator |
Luc Menichi Angers大, 講師
NAITO Takahito 東京大学, 数理科学研究科, 特別研究員(PD) (20724511)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | ストリングトポロジー / ループ空間 / 位相的場の理論 / 分類空間 / Eilenberg-Moore スペクトル系列 / 加群微分子 / Batalin-Vilkovisky作用素 / スペクトル系列 / Gorenstein空間 / 開閉位相的場の理論 / Batalin--Vilkovisky代数 / Batalin-Vilkovisky代数 |
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| Outline of Final Research Achievements |
We have investigated string topology initiated by Chas and Sullivan from a derived categorical point of view. In particular, the duals to the loop (co)products on the loop cohomology of Gorenstein spaces have been considered by using the torsion functor in appropriate derived categories on singular cochain algebras. We see that the Eilenberg-Moore spectral sequence converging to the relative loop homology works well in determining explicitly the loop homology of a homogeneous space. The second result concerns with string topology on classifying spaces in the sense of Chataur and Menichi. The Batalin-Vilkovisky algebra structure on the loop cohomology of the space is determined provided the cohomology of the given classifying space is isomorphic to a polynomial algebra. Surprisingly, in a more general case, the computation allows us to solve so-called the ``sign issue" on the prop which gives rise to homological conformal field theory on the loop homology on classifying spaces.
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Report
(6 results)
Research Products
(9 results)
