2018 Fiscal Year Final Research Report
| Project/Area Number |
15K04879
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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 | Nagoya City University |
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Principal Investigator |
Kamada Naoko 名古屋市立大学, 大学院システム自然科学研究科, 教授 (60419687)
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| Research Collaborator |
ISHII atsushi
KAMADA seiichi
KANENOBU taizo
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Keywords | 結び目 / 仮想結び目 / 不変量 |
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| Outline of Final Research Achievements |
We studied twisted knots, virtual knots, virtual doodle. Virtual knots correspond to stable equivalence classes of knots in thickened oriented closed surfaces. Twisted knots correspond to stable equivalence classes of knots in thickened closed surfaces. For some research methods of virtual knots, it is not easy to extend to those of twisted knots. We constructed the map from the set of twisted knots to that of virtual knots. As an application of this map, we defined an invariant of twisted knots and showed some applications. By extending this method, we introduced two normalization maps from a set of virtual knots to that of normal virtual knots. We showed some applications of them. We defined quandle invariants of virtual doodles by use of one of normalization maps. By extending one of normalization maps, we introduced the map from a set of virtual knots to that of mod m almost classical virtual knots. We showed some applications of this map.
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| Free Research Field |
幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
拡張結び目には結び目を代数的に表す様々な方法に視点をおいて定義されたものもある。結び目不変量の中にはそれらの表し方と関係している場合もあり広い観点からのそれらの構造や性質の理解につながる。その中にはカンドルなどの代数構造をもつ不変量もあり代数への応用も期待される。また、拡張結び目と曲面結び目の関係はよく知られている。結び目不変量で拡張結び目の不変量として解釈されるものもある。このような視点から結び目の新しい研究手法を導入できる可能性があり結び目の分類にも寄与すると考えられる。
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