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

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.

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.

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DOI : 10.5802/aif.3330
Classification : 57M25
Keywords: Knot, link, $\protect \operatorname{SU}(2)$-representation, Casson invariant, Casson–Lin invariant, multivariable signature, character variety, Alexander polynomial, Burau representation, Gassner representation
Mot clés : Noeud, entrelacs, représentation $\protect \operatorname{SU}(2)$, invariant de Casson, invariant de Casson–Lin, signature multivariée, variété de caractères, polynôme d’Alexander, représentation de Burau, représentation de Gassner
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
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Benard, Leo; Conway, Anthony. A multivariable Casson–Lin type invariant. Annales de l'Institut Fourier, Tome 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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