2011 Fiscal Year Final Research Report
Solving the unknotting conjecture in dimension four and its development
| Project/Area Number |
21540084
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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 | Hiroshima University |
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Principal Investigator |
MATUMOTO Takao 広島大学, 大学院理学研究科, 名誉教授 (50025467)
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| Co-Investigator(Kenkyū-buntansha) |
KAMADA Seiichi 広島大学, 大学院理学研究科, 教授 (60254380)
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| Project Period (FY) |
2009 – 2012
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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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| Research Abstract |
The smooth unknotting conjecture in dimension four is reduced to the case which is connected by a one-parameter family with one intersection point to the unknot, by assuming our Markov type theorem. Moreover, since the reduced case can be studied by a kind of tree type Cayley diagram for the corresponding word problem, the conjecture is expected to be proved in a near future.
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