2012 Fiscal Year Final Research Report
Topology of the embedding spaces via configuration space integrals, operads and the calculus of functors
| Project/Area Number |
23840015
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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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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| Project Period (FY) |
2011 – 2012
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| Keywords | 埋め込みの空間 / グラフ / オペラッド / 位相的Stiefel多様体 / ストリング・トポロジー / BV代数 / Hochschildホモロジー |
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| Research Abstract |
I continued the study of the spaces of embedding between spheres. I showed that the space fE called “the space of embeddings modulo immersions” is an iterated loop space of the topological Stiefel manifold. As applications I obtained;
(1) A BV-algebra structure on the homology of fE
(2) An alternative proof in terms of topological Stiefel manifolds of the fact that the “spinning” operation gives rise to an isomorphism of the lower dimensional homotopy groups of the embedding spaces.
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