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Reidemeister torsion for linear representations and Seifert surgery on knots

Research paper by Takahiro Kitayama

Indexed on: 24 Aug '09Published on: 24 Aug '09Published in: Mathematics - Geometric Topology



Abstract

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.