We provide necessary conditions on the Alexander polynomial of a knot in a homology sphere and on surgery coefficients for the surgered manifold to be a Seifert fibered space over . As an application, we show that no –surgery with 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 . The main tool is the abelian Reidemeister torsion.
"Reidemeister torsion of Seifert fibered homology lens spaces and Dehn surgery." Algebr. Geom. Topol. 7 (3) 1509 - 1529, 2007. https://doi.org/10.2140/agt.2007.7.1509