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.

13 pages, 3 figures; minor errors in Figures 2, 3 are corrected in V2

References in corpus (2)

• Positive knots have negative signature
• On LMO invariant constraints for cosmetic surgery and other surgery problems for knots in S^{3}

Cited by in corpus (3)

• Purely cosmetic surgeries and pretzel knots
• On constraints for knots to admit chirally cosmetic surgeries and their calculations
• On amphichirality of symmetric unions