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 a 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.