2009 Fiscal Year Final Research Report
Exceptional Dehn surgeries on hyperbolic knots and their arrangement
| Project/Area Number |
19540089
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Hiroshima University |
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Principal Investigator |
TERAGAITO Masakazu Hiroshima University, 大学院・教育学研究科, 准教授 (80236984)
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| Co-Investigator(Kenkyū-buntansha) |
GODA Hiroshi 東京農工大学, 大学院・共生科学技術研究院, 教授 (60266913)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 結び目 / 3次元多様体 / デーン手術 |
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| Research Abstract |
For a hyperbolic knot in the 3-sphere, Dehn surgery yielding a non-hyperbolic 3-manifold is called an exceptional Dehn surgery. There are essentially three types of exceptional Dehn surgery. In this project, we focused on lens space surgery and toroidal surgery, and obtained various results. In particular, I gave an infinite family of hyperbolic knots admitting toroidal surgeries corresponding to three consecutive integers, and an infinite family of hyperbolic knots admitting lens space surgery between toroidal surgeries.
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