A multivariable Casson-Lin type invariant

Léo Bénard; Anthony Conway

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arXiv · 1805.03050

A multivariable Casson-Lin type invariant

Léo Bénard·Anthony Conway

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Abstract

We introduce a multivariable Casson-Lin type invariant for links in $S^3$. This invariant is defined as a signed count of irreducible $\operatorname{SU}(2)$ representations of the link group with fixed meridional traces. For 2-component links with linking number one, the invariant is shown to be a sum of multivariable signatures. We also obtain some results concerning deformations of $\operatorname{SU}(2)$ representations of link groups.

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Léo Bénard, Anthony Conway. 2018-05-08. A multivariable Casson-Lin type invariant. https://arxiv.org/abs/1805.03050

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