Applications of the Casson-Walker invariant to the knot complement and the cosmetic crossing conjectures

Abstract

We give a rational surgery formula for the Casson-Walker invariant of a 2-component link in $S^3$ which is a generalization of Matveev-Polyak's formula. As application, we give more examples of non-hyperbolic L-space $M$ such that knots in $M$ are determined by their complements. We also apply the result for the cosmetic crossing conjecture.

14 pages, 2 figures

References in corpus (1)

• Cosmetic crossing conjecture for genus one knots with non-trivial Alexander polynomial

Cited by in corpus (1)

• On the Cosmetic Crossing Conjecture for Special Alternating Links