2016 Fiscal Year Final Research Report
Solving the smooth unknotting conjecture in dimension four and its development
| Project/Area Number |
24540082
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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 University |
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Principal Investigator |
Matumoto Takao 京都大学, 数理解析研究所, 特任教授 (50025467)
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Keywords | ２次元結び目 / ２次元ブレイド / ４次元トポロジー / 数学史 |
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| Outline of Final Research Achievements |
The smooth unknotting conjecture in dimension four is reduced to the case which is connected by a one-parameter family of braided surfaces with at most one intersection point to the 2-dimensional braid representing an unknot, by assuming our writing Markov type theorem.
Moreover, in this case we do not know that the given knot is trivial yet but we see that its connected sum with the trivial torus knot is diffeomorphic to the trivial torus knot.
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| Free Research Field |
数学とくに幾何学・多様体論・トポロジーなど
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