Study on local moves of knots with application to polymer topology
| Project/Area Number |
24540089
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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 City University |
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Principal Investigator |
KANENOBU Taizo 大阪市立大学, 大学院理学研究科, 教授 (00152819)
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| Co-Investigator(Kenkyū-buntansha) |
河内 明夫 大阪市立大学, 大学院理学研究科, 特任教授 (00112524)
田山 育男 大阪市立大学, 大学院理学研究科, 研究員 (00382036)
森内 博正 近畿大学, 医学部, 講師 (20453128)
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 結び目 / 絡み目 / バンド手術 / 交差交換 / 多項式不変量 / DNA結び目 / 整合的バンド手術 / H(2)移動 / 仮想弧 / ２次元リボン結び目 / ジョーンズ多項式 / 交差交換距離 / 整合的バンド距離 / 絡み目解消数 / SH(3)移動 |
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| Outline of Final Research Achievements |
We studied several local moves on knots and links such as a band surgery, crossing change, and SH(3)-move. We introduce further criteria to estimate the lower bound of the Gordian distances between two knots or links, which use the special values of the Jones, Q, and HOMFLYPT polynomials. Also, we gave criteria for the determinants between two links which are related by a band surgery, which come from the known criteria between two knots which are related by a crossing change. Then we gave a table of SH(3)-Gordian distances between knots with up to 7 crossings, we improved a table of H(2)-Gordian distances between knots with up to 7 crossings, we gave a table of Gordian distances between 2-component links with up to 6 crossings, and we improved a table of unknotting numbers of knots with up to 12 crossings.
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Report
(6 results)
Research Products
(40 results)
