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

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 an appropriate assumption on the Reidemeister torsion of the universal abelian covering of $M$ implies $q=\pm 1$, if $M$ is a Seifert fibered space.