2013 Fiscal Year Final Research Report
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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| Keywords | ３次元多様体論 / デーン手術 |
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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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Research Products
(13 results)
