| Project/Area Number |
16K05145
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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 | Gifu University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | リボン結び目 / 曲面 / 結び目 / 対称和 / 位相幾何学 |
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| Outline of Final Research Achievements |
The purpose of this research is to characterize and classify ribbon knots in three-dimensional space by examining topological properties of curves appearing as the intersection of surfaces in the knot complement. It is expected that results can be obtained by examining the property of the curves that appears at the intersection of surfaces, which is a basic method of topology.
In this research, I studied a ribbon knot which is the main research object by studying surfaces in the knot complement. In particular, I studied a symmetric union, which is an example of a ribbon knot. As a result, I characterized surfaces in the knot complement in the case of composite knots or satellite knots for a symmetric union with minimum twist number one.
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| Academic Significance and Societal Importance of the Research Achievements |
補空間の曲面は，比較的扱いやすい多項式不変量に比べて，結び目のより詳細な情報をもつことが予想される。3次元空間における結び目の補空間の曲面を直接調べることによるスライス結び目の研究は，これまであまり行われていない。そのようなことから，本研究は成果はスライス結び目の幾何学的手法を用いた新たな研究手法に挑戦することにおいて，意義があると思われる。
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