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.

6 pages, 1 figure