no. 3
A multivariable Casson–Lin type invariant
[Un invariant de Casson–Lin multivarié]
Benard, Leo1 ; Conway, Anthony2
1 Institut Mathématique de Jussieu-Paris Rive Gauche, Sorbonne Université, France
2 Department of Mathematics, Durham University, United Kingdom
Annales de l'Institut Fourier, Tome 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.

Reçu le :
Révisé le :
Accepté le :
Publié le :
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
Mots-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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     title = {A multivariable {Casson{\textendash}Lin} type invariant},
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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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