Two-bridge knots admit no purely cosmetic surgeries
Geometric Topology
2021-11-10 v2
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 Casson invariant.
Keywords
Cite
@article{arxiv.1909.02340,
title = {Two-bridge knots admit no purely cosmetic surgeries},
author = {Kazuhiro Ichihara and In Dae Jong and Thomas W. Mattman and Toshio Saito},
journal= {arXiv preprint arXiv:1909.02340},
year = {2021}
}
Comments
13 pages, 3 figures; minor errors in Figures 2, 3 are corrected in V2