Cosmetic surgery conjecture for alternating knots
| Project/Area Number |
26400100
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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 | Nihon University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | ３次元多様体 / デーン手術 / 交代結び目 / 低次元トポロジー / 矯飾的手術 / ランダム絡み目 / フォックス彩色 / 整数彩色 / 最小彩色数 / 結び目 / 左不変順序付不可能手術 / ねじれトーラス結び目 / モンテシノス結び目 / 境界スロープ |
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| Outline of Final Research Achievements |
In the study of knots in the 3-space, their complements have played important roles. In fact, the pair of complements of equivalent knots must be homeomorphic. In contrast, Gordon and Luecke have proved that the knots with homeomorphic complements must be equivalent. The key of their proof is an operation called Dehn surgery on knots. Actually, they showed that the trivial and any non-trivial Dehn surgeries on a non-trivial knot give non-homeomorphic pair of 3-manifolds. This theorem can be generalized to the conjecture on knots in general manifolds, which is now called the Cosmetic Surgery Conjecture. In this research project, we have focused on the Dehn surgeries on alternating knots in 3-space, and obtained some partial answer to the conjecture. Also given are some related results on 3-manifolds and knots and links.
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Report
(5 results)
Research Products
(43 results)
