Reidemeister torsion for linear representations and Seifert surgery on knots

Details Reidemeister torsion for linear representations and Seifert surgery on knots Reidemeister torsion for linear representations and Seifert surgery on knots

2008-10-10

arxiv.org/abs/0810.1912v3

Topology Appl. 156 (2009) 2496-2503

Mathematics

Geometric Topology

9 pages, 2 figures; improvements in the last section; to appear in Topology and its Applications

Scientific paper

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 $S^2$. 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.

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