Estimates of knot invariants via diagrams and geometrical sence of them
| Project/Area Number |
20740035
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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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) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 位相幾何 / 結び目理論 / ラスムッセン不変量 / 正または負の絡み目 / コバノフホモロジー / ベネカン型評価式 / 鏡像 / ベネカン不等式 / オジュバットとサボーの結び目不変量 / 絡み目のフレアーホモロジー / ホップ絡み目の連結和 / 鏡像に関する歪対称性 / 正の絡み目 / 絡み目のコボルディズム / 4次元トポロジー / 3次元多様体 |
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| Research Abstract |
We have never found any formula to determine the minimum number of crossing changes needed to unknot any given knot. In this research, we estimate this minimum number via a diagram of the knot, more strictly than known results. Essentially, we estimate the four-genus, the Rasmussen invariant, and Ozsvath and Szabo's invariant.
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Report
(6 results)
Research Products
(7 results)
