• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2015 Fiscal Year Final Research Report

Geometric and algebraic approach to the embedding spaces

Research Project

  • PDF
Project/Area Number 25800038
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionShinshu 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

トポロジー

URL: 

Published: 2017-05-10  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi