Geometric and algebraic approach to the embedding spaces
| Project/Area Number |
25800038
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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 | Shinshu University |
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Principal Investigator |
SAKAI Keiichi 信州大学, 学術研究院理学系, 助教 (20466824)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 埋め込みの空間 / グラフ / 配置空間 / ループ空間 / オペラッド / 代数的トポロジー / 埋め込みのなす空間 / 分類空間 / グラフ複体 / トポロジー / Haefliger不変量 / 多重ループ空間 / ジェネリックはめ込み |
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| Outline of Final Research Achievements |
The Haefliger invariant is known to classify the isotopy classes of embeddings of spheres in a dimension. I have described the Haefliger invariant using certain integrals over configuration spaces associated with graph cocycles, and I have shown that the Haefliger invariant behaves similarly to the finite type invariants. As a byproduct I have obtained a generic regular homotopy invariant of immersions with some conditions.
Based on the fact that the space of embeddings of spheres is a multi-fold loop space, I have given its "delooping" using the topological Stiefel manifolds, and I have obtained a homotopy-theoretic interpretation of the Haefliger's classification of the embeddings of spheres.
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Report
(4 results)
Research Products
(8 results)
