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

For a knot K in a homology 3-sphere Σ, let M be the result of 2/q-surgery on K, and let X be the universal abelian covering of M. Our first theorem is that if the first homology of X is finite cyclic and M is a Seifert fibered space with N≥3 singular fibers, then N≥4 if and only if the first homology of the universal abelian covering of X is infinite. Our second theorem is that under an appropriate assumption on the Alexander polynomial of K, if M is a Seifert fibered space, then q=±1 (i.e. integral surgery).