| Project/Area Number |
21654011
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Hiroshima University |
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Principal Investigator |
MAKOTO Sakuma 広島大学, 大学院・理学研究科, 教授 (30178602)
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| Co-Investigator(Kenkyū-buntansha) |
SEIICHI Kamada 広島大学, 大学院・理学研究科, 教授 (60254380)
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| Co-Investigator(Renkei-kenkyūsha) |
MASAKAZU Teragaito 広島大学, 大学院・教育学研究科, 教授 (80236984)
KEN. ICHI Ohshika 大阪大学, 大学院・理学研究科, 教授 (70183225)
TOSHIYUKI Sugawa 東北大学, 大学院・情報科学研究科, 教授 (30235858)
YASUSHI Yamashita 奈良女子大学, 理学部, 教授 (70239987)
HIROTAKA Akiyoshi 近畿大学, 理工学部, 准教授 (80397611)
HIROKI Sumi 大阪大学, 大学院・理学研究科, 准教授 (40313324)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,740,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2009: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | 離散群 / 非離散表現 / 2橋結び目 / 2橋絡み目 / 錐多様体 / small cancellation theory / McShaneの等式 / free period / エンド不変量 / 結び目群 / 橋分解 |
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| Research Abstract |
We completely determined those simple loops on the 2-bridge spheres of 2-bridge links to be null-homotopic or peripheral in the link complements. We also completely determined when two simple loops on the 2-bridge spheres of 2-bridge links to be homotopic in the link complements. As an application of these results, we established a variation of McShane' s identity for 2-bridge links, which gives a formula to express the modulus of the cusp of a 2-bridge link in terms of the complex translation lengths of closed geodesics
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