Two-bridge knots admit no purely cosmetic surgeries
| Autor: | Kazuhiro Ichihara, Toshio Saito, Thomas W. Mattman, In Dae Jong |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Fibered knot Geometric Topology (math.GT) Type (model theory) Primary 57M27 Secondary 57M25 Bridge (interpersonal) Casson invariant Mathematics::Geometric Topology Mathematics - Geometric Topology Knot (unit) FOS: Mathematics Geometry and Topology Signature (topology) Mathematics::Symplectic Geometry Mathematics |
| Popis: | We show that two-bridge knots and alternating fibered knots admit no purely cosmetic surgeries, i.e., no pair of distinct Dehn surgeries on such a knot produce 3-manifolds that are homeomorphic as oriented manifolds. Our argument, based on a recent result by Hanselman, uses several invariants of knots or 3-manifolds; for knots, we study the signature and some finite type invariants, and for 3-manifolds, we deploy the $SL(2,\mathbb{C})$ Casson invariant. 13 pages, 3 figures; minor errors in Figures 2, 3 are corrected in V2 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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