Reidemeister torsion for linear representations and Seifert surgery on knots

Takahiro Kitayama

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arXiv · 0810.1912

Reidemeister torsion for linear representations and Seifert surgery on knots

Takahiro Kitayama

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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.

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Takahiro Kitayama. 2009-08-24. Reidemeister torsion for linear representations and Seifert surgery on knots. https://arxiv.org/abs/0810.1912

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