2023 Fiscal Year Final Research Report
Construction of polynomial invariants for knotoids
| Project/Area Number |
17K05255
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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 | Yamaguchi University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2024-03-31
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| Keywords | knotoid / 結び目 / 結び目理論 |
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| Outline of Final Research Achievements |
The principal investigator studied "knotoids" which are represented by "open" knot diagrams in a surface and successfully constructed the Jones polynomial, the HOMFLY polynomial and the Kauffman polynomial for knotoids, which correspond to the three famous polynomial invariants in knot theory.
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| Free Research Field |
結び目理論
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| Academic Significance and Societal Importance of the Research Achievements |
開発されたknotoidの多項式不変量はknotoidの分類のみならず特質の解明に役立つ。また，結び目理論への応用やその形状と深く関わる他分野，特に，DNA結び目と繋がる生物分野や高分子化合物を対象とする物理・化学分野の諸問題について解決への寄与が期待できる。さらには，その先に続く工学的・農学的分野の応用へと波及し，我々の実生活に好影響を与えるのではないかと想像される・
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