| 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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| 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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