Toward the complete classification of exceptional surgeries on alternating knots
| Project/Area Number |
23740061
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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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) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | ３次元多様体論 / デーン手術 / トポロジー / 3次元多様体論 |
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| Research Abstract |
A space locally modeled on the 3-dimensional Euclidean space is called a 3-manifold. To study their relationships, an operation called Dehn surgery has been focused and studied. Among the study, it was shown that there are only finitely many Dehn surgeries on a hyperbolic knot yield non-hyperbolic manifolds. Here a knot is called hyperbolic if its complement admits a hyperbolic structure. Now these finitely many exceptions are called exceptional surgeries, and have been studied in detail. In fact, related to Knot Theory, on hyperbolic knots in the 3-dimensional Euclidean space, the classification of exceptional surgeries have been studied. In the currently reported study, one of the most well-known and well-studied class of knots, called alternating knots, was concerned, and actually the complete classification of exceptional surgeries on hyperbolic alternating knots has been established.
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Report
(4 results)
Research Products
(36 results)
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[Presentation] Exceptional surgeries on alternating knots
Author(s)
Kazuhiro Ichihara and Hidetoshi Masai
Organizer
The International Workshop on Numerical Verification and its Applications 2014
Place of Presentation
Waseda University, Nishiwaseda Campus, Building 63, 2nd floor, Room 05.
Related Report
Invited
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