Reidemeister torsion of Seifert fibered homology lens spaces and Dehn surgery

Kadokami, Teruhisa

doi:10.2140/agt.2007.7.1509

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Reidemeister torsion of Seifert fibered homology lens spaces and Dehn surgery

Teruhisa Kadokami

Algebraic & Geometric Topology 7 (2007) 1509–1529

DOI: 10.2140/agt.2007.7.1509

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

References

Publication

Received: 24 May 2007

Revised: 20 September 2007

Published: 14 November 2007

Authors

Teruhisa Kadokami
Osaka City University Advanced Mathematical Institute Sugimoto 3-3-138, Sumiyoshi-ku Osaka 558-8585 Japan

Volume 7, issue 3 (2007)