Seifert surgery on knots via Reidemeister torsion and Casson-Walker-Lescop invariant

Abstract

For a knot $K$ with $\Delta_K(t)\doteq t^2-3t+1$ in a homology $3$-sphere, let $M$ be the result of $2/q$-surgery on $K$. We show that appropriate assumptions on the Reidemeister torsion and the Casson-Walker-Lescop invariant of the universal abelian covering of $M$ imply $q=\pm 1$, if $M$ is a Seifert fibered space.