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Abstract
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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.
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Keywords
Dehn surgery, Seifert fibered space, homology lens space,
Reidemeister torsion, Alexander polynomial
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Mathematical Subject Classification 2000
Primary: 55R55, 19J10, 57Q10, 57M25
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Publication
Received: 24 May 2007
Revised: 20 September 2007
Published: 14 November 2007
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