8,189 research outputs found
Reidemeister torsion for linear representations and Seifert surgery on knots
We study an invariant of a 3-manifold which consists of Reidemeister torsion
for linear representations which pass through a finite group. We show a Dehn
surgery formula on this invariant and compute that of a Seifert manifold over
. As a consequence we obtain a necessary condition for a result of Dehn
surgery along a knot to be Seifert fibered, which can be applied even in a case
where abelian Reidemeister torsion gives no information.Comment: 9 pages, 2 figures; improvements in the last section; to appear in
Topology and its Application
Twisted Alexander polynomials and incompressible surfaces given by ideal points
We study incompressible surfaces constructed by Culler-Shalen theory in the
context of twisted Alexander polynomials. For a st cohomology class of a
-manifold the coefficients of twisted Alexander polynomials induce regular
functions on the -character variety. We prove that if an
ideal point gives a Thurston norm minimizing non-separating surface dual to the
cohomology class, then the regular function of the highest degree has a finite
value at the ideal point.Comment: 10 pages, to appear in "The special issue for the 20th anniversary",
the Journal of Mathematical Sciences, the University of Toky
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