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

We give a rational surgery formula for the Casson-Walker invariant of a 2-component link in S3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^{3}$$\end{document} 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.