#### Volume 7, issue 3 (2007)

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Reidemeister torsion of Seifert fibered homology lens spaces and Dehn surgery

Algebraic & Geometric Topology 7 (2007) 1509–1529
##### 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.

##### Keywords
Dehn surgery, Seifert fibered space, homology lens space, Reidemeister torsion, Alexander polynomial
##### Mathematical Subject Classification 2000
Primary: 55R55, 19J10, 57Q10, 57M25