Geometry on concordance invariants of knots and links
| Project/Area Number |
24540074
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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 University |
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Principal Investigator |
Kawamura Tomomi 名古屋大学, 多元数理科学研究科, 准教授 (40348462)
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| Project Period (FY) |
2012-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 結び目と絡み目 / 結び目と絡み目の射影図 / ラスムッセン不変量 / オジュバットとサボーの結び目不変量 / プレッツェル結び目 / ザイフェルト曲面 / 種数あるいはオイラー数 / 橋の架け替え / 種数 / ４次種数 / 絡み目コンコルダンス不変量 / 絡み目のホモロジー / オイラー数 / スライスオイラー数 / コバノフホモロジー / フレアーホモロジー / オジュバットとサボーの不変量 / ザイフェルト円周 / 結び目コンコルダンス不変量 / 絡み目のコボルディズム / 絡み目のスライスオイラー数 / ベネカン不等式 / ベネカン型不等式 |
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| Outline of Final Research Achievements |
A knot or link is a closed curve or its copies in the 3-dimensional space. An invariant of a knot or link is the number or something representing how complex it is. Many invariants have been constructed.
In this research, we determine the Rasmussen invariant and the Ozsvath-Szabo invariant for certain pretzel knots. Furthermore we show a bridge-replacing move induced on knot diagrams is as useful in computing the Euler characteristic of a link, a kind of link invariants, as the genus of a knot, a kind of knot invariants.
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Report
(7 results)
Research Products
(2 results)
