Two-bridge knots admit no purely cosmetic surgeries
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2019
- DOI:
- 10.48550/arXiv.1909.02340
- arXiv:
- arXiv:1909.02340
- Bibcode:
- 2019arXiv190902340I
- Keywords:
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- Mathematics - Geometric Topology;
- Primary 57M27;
- Secondary 57M25
- E-Print:
- 13 pages, 3 figures