A multivariable Casson–Lin type invariant

Benard, Leo; Conway, Anthony

doi:10.5802/aif.3330

A multivariable Casson–Lin type invariant [ Un invariant de Casson–Lin multivarié ]

Benard, Leo ; Conway, Anthony

Annales de l'Institut Fourier, Tome 70 (2020) no. 3, pp. 1029-1084.

Résumé
Abstract

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.

Reçu le : 2018-08-30
Révisé le : 2019-03-27
Accepté le : 2019-09-18
Publié le : 2020-06-26

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--Lin type invariant},
     journal = {Annales de l'Institut Fourier},
     pages = {1029--1084},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {70},
     number = {3},
     year = {2020},
     doi = {10.5802/aif.3330},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2020__70_3_1029_0/}
}

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/item/AIF_2020__70_3_1029_0/

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