Reidemeister torsion for linear representations and Seifert surgery on knots

Takahiro Kitayama

Reidemeister torsion for linear representations and Seifert surgery on knots

Geometric Topology 2009-08-24 v3

Authors: Takahiro Kitayama

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.

Keywords

Reidemeister torsion linear representation Dehn surgery Seifert manifold knot 3-manifold invariant

Cite

@article{arxiv.0810.1912,
  title  = {Reidemeister torsion for linear representations and Seifert surgery on knots},
  author = {Takahiro Kitayama},
  journal= {arXiv preprint arXiv:0810.1912},
  year   = {2009}
}

Comments

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

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