Reidemeister torsion of Seifert fibered homology lens spaces and Dehn surgery

Abstract

We provide necessary conditions on the Alexander polynomial of a knot $K$ in a homology sphere and on surgery coefficients $p∕q$ for the surgered manifold to be a Seifert fibered space over $S^2$. As an application, we show that no $p∕q$–surgery with $p>3$ on a knot in a homology sphere with the same Alexander polynomial as the figure eight knot can produce a Seifert fibered space with base $S^2$. The main tool is the abelian Reidemeister torsion.