Geodesic
Reidemeister torsion of Seifert fibered homology lens spaces and Dehn surgery
Kadokami, Teruhisa1
1Osaka City University Advanced Mathematical Institute, Sugimoto 3-3-138, Sumiyoshi-ku, Osaka 558-8585, Japan
Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1509-1529
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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 S2. 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 S2. The main tool is the abelian Reidemeister torsion.

DOI : 10.2140/agt.2007.7.1509
Keywords: Dehn surgery, Seifert fibered space, homology lens space, Reidemeister torsion, Alexander polynomial

Kadokami, Teruhisa  1

1 Osaka City University Advanced Mathematical Institute, Sugimoto 3-3-138, Sumiyoshi-ku, Osaka 558-8585, Japan 
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Kadokami, Teruhisa. Reidemeister torsion of Seifert fibered homology lens spaces and Dehn surgery. Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1509-1529. doi: 10.2140/agt.2007.7.1509

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