no. 3

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 : https://doi.org/10.5802/aif.3330
Classification : 57M25
Mots clés : Noeud, entrelacs, représentation SU(2), invariant de Casson, invariant de Casson–Lin, signature multivariée, variété de caractères, polynôme d’Alexander, représentation de Burau, représentation de Gassner 
@article{AIF_2020__70_3_1029_0,
     author = {Benard, Leo and Conway, Anthony},
     title = {A multivariable {Casson{\textendash}Lin} type invariant},
     journal = {Annales de l'Institut Fourier},
     pages = {1029--1084},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {70},
     number = {3},
     year = {2020},
     doi = {10.5802/aif.3330},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3330/}
}
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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