2010 Fiscal Year Final Research Report
Global Theory of Singularities of Differentiable Maps and its Applications
| Project/Area Number |
19340018
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Kyushu University |
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Principal Investigator |
SAEKI Osamu Kyushu University, 大学院・数理学研究院, 教授 (30201510)
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| Co-Investigator(Kenkyū-buntansha) |
SAKUMA Kazuhiro 近畿大学, 理工学部, 教授 (80270362)
OHMOTO Toru 北海道大学, 大学院・理学研究院, 准教授 (20264400)
IWASE Norio 九州大学, 大学院・数理学研究院, 教授 (60213287)
KOBAYASHI Mahito 秋田大学, 大学院・工学資源学研究科, 准教授 (10261645)
YAMAMOTO Minoru 愛知教育大学, 教育学部, 講師 (40435475)
ANDO Yoshifumi 山口大学, 大学院・理工学研究科, 教授 (80001840)
TAKAYAMA Haruko 九州大学, 大学院・数理学研究院, 助教 (90274430)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKASE Masamichi 信州大学, 理学部, 准教授 (30447718)
YAMAMOTO Takahiro 九州産業大学, 工学部, 講師 (60435972)
TAKATA Toshie 九州大学, 大学院・数理学研究院, 准教授 (40253398)
OKUMA Tomohiro 山形大学, 地域教育文化学部, 准教授 (00300533)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 微分トポロジー / 大域的特異点論 / 可微分構造 / 同境 / 特異ファイバー / ホモトピー原理 / 多様体対 / 可視化 |
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| Research Abstract |
We studied singularities of differentiable maps between manifolds from a global point of view and obtained various new results about such singularities and differential topological properties of manifolds. For example, it is known that many 4-dimensional topological manifolds admit infinitely many differentiable structures, and we have proved that among them there is only one such structure that allows the existence of a differentiable map with the simplest singularities. We also discovered some examples of global results that can be used to study local singularities. In this manner, we have clarified the deep relationship between the singularities (or singular fibers) of maps and the cobordism classes of manifolds and maps, obtaining a lot of explicit and concrete results.
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[Book] 技術に生きる現代数学2008
Author(s)
若山正人編, 若山正人, 谷口説男, 福本康秀, 金子昌信, 二宮嘉行, 佐伯修著
Total Pages
175-204
Publisher
岩波書店
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