Geometric and algebraic approach to the embedding spaces

2015 Fiscal Year Final Research Report

• Project/Area Number: 25800038
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Shinshu University
• Principal Investigator: SAKAI Keiichi 信州大学, 学術研究院理学系, 助教 (20466824)
• Project Period (FY): 2013-04-01 – 2016-03-31
• 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

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.

Free Research Field

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