2023 Fiscal Year Final Research Report
Mathematical theory of knots with application to polymer topology
| Project/Area Number |
17K05259
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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 | Osaka Metropolitan University (2022-2023)
Osaka City University (2017-2021) |
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Principal Investigator |
Kanenobu Taizo 大阪公立大学, 大学院理学研究科, 特任教授 (00152819)
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| Project Period (FY) |
2017-04-01 – 2024-03-31
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| Keywords | 結び目 / 絡み目 / バンド手術 / 交差交換 / H(2)移動 / 4移動 |
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| Outline of Final Research Achievements |
We studied several local moves on knots and links such as a coherent band surgery, a crossing change, an H(2)-move, and 4-move, and related topics on knot theory, keeping in mind research on DNA recombination and the topological structure of polymers. In particular, we studied the unknotting number of a knot and also the distance between two knots, which is the minimum number of the local moves needed to deform one knot to the other, where we applied knot polynomial invariants. We also attempt to create tables of unknotting numbers and distances for knots with small crossing number.
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| Free Research Field |
数物系科学
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| Academic Significance and Societal Importance of the Research Achievements |
DNA分子は，複製，転写，組み換えという遺伝現象の核心をなす過程においてトポロジー(位相的な構造)が変化するが，それはトポイソメラーゼとよばれる酵素の働きによるものである.トポイソメラーゼとは，DNA の鎖を切断して，さらに結合するというような操作をおこなう酵素の総称である.トポイソメラーゼは環状のDNA に対して交差交換やバンド手術のような作用をすると考えられており，結び目，絡み目の局所変形の研究の成果がDNA等の高分子の研究に応用されることが期待される.
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