2000 Fiscal Year Final Research Report Summary
Homotopy theoretic study of singularities of smooth mappings
| Project/Area Number |
11640081
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Yamaguchi University |
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Principal Investigator |
ANDO Yoshifumi Yamaguchi University.Faculty of Science Professor, 理学部, 教授 (80001840)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAZAWA Yazuyuki Yamaguchi University. Faculty of Science Assistant, 理学部, 助手 (60263761)
KOMIYA Katuhiro Yamaguchi University. Faculty of Science Professor, 理学部, 教授 (00034744)
MIYOSHI Tetuhiko Yamaguchi University. Faculty of Science Professor, 理学部, 教授 (60040101)
SATO Yoshihisa Yamaguchi University. Faculty of Education Lecturer, 教育学部, 講師 (90231349)
WATANABE Tadashi Yamaguchi University. Faculty of Education Professor, 教育学部, 教授 (10107724)
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| Project Period (FY) |
1999 – 2000
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| Keywords | smooth maps / singularity / fold map / Morin map / jet space / homotopy |
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| Research Abstract |
In this research we have studied global properties of simple singularities of smooth maps, in particular, fold singularities and Morin singularities from the viewpoint of homotopy theory. We have studied the set of fold-eobordism classes of fold-maps of degree m, and established a relation between this cobordism set and the set of homotopy classes to the space of base point preserving maps of degree m of spheres. In this study a homotopy principle for Morin singularities, which has been established in our research, has played an important role.
Furthermore, we have determinod the homotopy type of the subspace in 2 jet space associated with fold maps. This reduces the existence problem of fold-maps toa homotopy theoretic problem of finding sections of fiber bundles.
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