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Existence and classification problems of equivariant maps preserving orbit structures

保留轨道结构的等变图的存在性及分类问题

基本信息

批准号：
23540101
负责人：
IKUMITSU Nagasaki
金额：
$ 2.75万
依托单位：
Kyoto Prefectural University of Medicine
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2011
资助国家：
日本
起止时间：
2011 至 2013
项目状态：
已结题

项目摘要

In this research, we studied the existence and classification problems of isovariant maps from the viewpoint of the Borsuk-Ulam theorem and the o-minimal topology. The isovariant map between G-spaces is an equivariant map preserving their orbit structures. We obtain the following results: (1) We found new families of finite groups for which the isovariant Borsuk-Ulam theorem holds. This provides a necessary condition for the existence of isovariant maps. (2) In the classification problem, we consider isovariant homotopy classes of isovariant maps from a closed free G-manifolds to a sphere of a representation space, and in suitable situation, we obtain that the multidegree classifies isovariant homotopy classes. This result is a generalization of the classical Hopf theorem.

在这项研究中，我们从Borsuk-Ulam定理和o-极小拓扑的角度研究了等变映射的存在性和分类问题。G-空间之间的等变映射是保持G-空间轨道结构的等变映射。我们得到了如下结果：(1)我们发现了新的有限群族，对这些有限群族，等变的Borsuk-Ulam定理成立。这为等变映射的存在提供了必要条件。(2)在分类问题中，我们考虑了从闭自由G-流形到表示空间的球面的等变映射的等变同伦类，在适当的情况下，我们得到了等变同伦类的多度分类。这一结果是经典Hopf定理的推广。