A multivariable Casson–Lin type invariant
Annales de l'Institut Fourier, Volume 70 (2020) no. 3, pp. 1029-1084.

We introduce a multivariable Casson–Lin type invariant for links in S 3 . This invariant is defined as a signed count of irreducible 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 SU(2) representations of link groups.

Nous définissons un invariant de Casson–Lin multivarié. Cet invariant est défini comme un comptage signé de représentations irréductibles SU(2) du groupe de l’entrelacs, avec traces méridionales fixées. Pour les entrelacs à 2 composantes avec coefficient d’enlacement égal à un, nous montrons que l’invariant est égal à une somme de signatures multivariées. Nous obtenons également des résultats concernant les déformations de représentations SU(2) de groupes d’entrelacs.

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DOI: 10.5802/aif.3330
Classification: 57M25
Keywords: Knot, link, SU(2)-representation, Casson invariant, Casson–Lin invariant, multivariable signature, character variety, Alexander polynomial, Burau representation, Gassner representation
Benard, Leo 1; Conway, Anthony 2

1 Institut Mathématique de Jussieu-Paris Rive Gauche, Sorbonne Université, France
2 Department of Mathematics, Durham University, United Kingdom
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Benard, Leo; Conway, Anthony. A multivariable Casson–Lin type invariant. Annales de l'Institut Fourier, Volume 70 (2020) no. 3, pp. 1029-1084. doi : 10.5802/aif.3330. https://aif.centre-mersenne.org/articles/10.5802/aif.3330/

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