2013 Fiscal Year Final Research Report
Existence and classification problems of equivariant maps preserving orbit structures
| Project/Area Number |
23540101
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kyoto Prefectural University of Medicine |
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Principal Investigator |
IKUMITSU Nagasaki 京都府立医科大学, 医学(系)研究科(研究院), 教授 (50198305)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAKAMI Tomohiro 和歌山大学, 教育学部, 准教授 (20234023)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 変換群 / 同変トポロジー / Borsuk-Ulam型定理 / 等変写像 / 順序極小構造 |
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| Research Abstract |
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.
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