Research on low-dimensional manifold with handle diagram
| Project/Area Number |
26800031
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | University of Tsukuba |
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Principal Investigator |
TANGE Motoo 筑波大学, 数理物質系, 助教 (70452422)
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| Research Collaborator |
ABE Tetsuya 立命館大学, 数理科学科, 数学嘱託講師 (00614009)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | エキゾチック微分構造 / コルク / ホモロジー球面 / スライスリボン予想 / レンズ空間手術 / コルクツイスト / ホモロジー３球面 / 有理４球体 / L-空間 / 異種微分構造 / ４次元多様体 / ヒーゴールフレアホモロジー / ケーブル結び目 / 有理ホモロジー4球体 / スライス結び目 / 4次元多様体 / 3次元多様体 / リボン結び目 |
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| Outline of Final Research Achievements |
In this research, I studied localization of exotic differential structures in 4-dimensional manifold. This phenomenon is due to the interesting existence of plug or cork. As a result, I obtained concrete construction of plug for Fintushel-Stern knot-surgery and its applications. I also constructed finite order Stein corks for the first time. In the later research, these corks have irreducible condition. Gompf constructed infinite order corks, I focus on some finite property for OS-invariants and generalized to the property which any infinite cork satisfies. In contrast to order two cork, this property is a remarkable nature. In the research of the Slice-Ribbon conjecture we found a close relationship between the slice-ribbon conjecture and handle theory. From the point of view, we give a sufficient condition for slice knot to be a ribbon by using a handle diagram with respect to the slice knot. The difficulty of slice-ribbon conjecture can rephrase the one of handle theory.
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Report
(5 results)
Research Products
(37 results)
