2013 Fiscal Year Final Research Report
The spaces of regular maps and the applications of real singularity theory to homotopy theory
| Project/Area Number |
23540079
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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 | The University of Electro-Communications |
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Principal Investigator |
YAMAGUCHI Kohhei 電気通信大学, 情報理工学(系)研究科, 教授 (00175655)
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| Co-Investigator(Kenkyū-buntansha) |
KIDA Masanari 東京理科大学, 理学部, 教授 (20272057)
YAMADA Yuuichi 電気通信大学, 大学院・情報理工学研究科, 教授 (30303019)
OHNO Masahiro 電気通信大学, 大学院・情報理工学研究科, 准教授 (70277820)
SHIMAKWA Kazuhisa 岡山大学, 自然科学研究科, 教授 (70109081)
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| Project Period (FY) |
2011 – 2013
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| Keywords | ホモトピー型 / 代数的写像 / 実代数幾何学 / 正則写像 / 写像空間 / 多様体 / ホモロジー群 / 多様体手術 |
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| Research Abstract |
The main purpose of this research is to investigate the generalization of the work of spaces of rational functions due to G. Segal (Acta Math., 1979). In this research, we consider the topology of the mapping space Map(M,N) when M and N are manifolds with dim M >1, and we mainly study the case that M and N are real projective spaces. In this case, we try to approximate it by a finite dimensional subspace Alg(M,N) of algebraic maps (or regular maps) which are represented by polynomials.
In particular, we can determine the explicit dimension of approximating homotopy type of it by the joint work with A. Kozlowski (Warsaw University) .
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