Seifert surgery on knots via Reidemeister torsion and Casson-Walker-Lescop invariant

Teruhisa Kadokami; Noriko Maruyama; Tsuyoshi Sakai

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arXiv · 1408.5356

Seifert surgery on knots via Reidemeister torsion and Casson-Walker-Lescop invariant

Teruhisa Kadokami·Noriko Maruyama·Tsuyoshi Sakai

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Abstract

For a knot $K$ with $\Delta_K(t)\doteq t^2-3t+1$ in a homology $3$-sphere, let $M$ be the result of $2/q$-surgery on $K$. We show that appropriate assumptions on the Reidemeister torsion and the Casson-Walker-Lescop invariant of the universal abelian covering of $M$ imply $q=\pm 1$, if $M$ is a Seifert fibered space.

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Teruhisa Kadokami, Noriko Maruyama, Tsuyoshi Sakai. 2014-08-22. Seifert surgery on knots via Reidemeister torsion and Casson-Walker-Lescop invariant. https://arxiv.org/abs/1408.5356

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