| 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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| 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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