We introduce a multivariable Casson–Lin type invariant for links in . This invariant is defined as a signed count of irreducible 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 representations of link groups.
Nous définissons un invariant de Casson–Lin multivarié. Cet invariant est défini comme un comptage signé de représentations irréductibles 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 de groupes d’entrelacs.
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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
CC-BY-ND 4.0
@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/}
}
TY - JOUR AU - Benard, Leo AU - Conway, Anthony TI - A multivariable Casson–Lin type invariant JO - Annales de l'Institut Fourier PY - 2020 SP - 1029 EP - 1084 VL - 70 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3330/ DO - 10.5802/aif.3330 LA - en ID - AIF_2020__70_3_1029_0 ER -
%0 Journal Article %A Benard, Leo %A Conway, Anthony %T A multivariable Casson–Lin type invariant %J Annales de l'Institut Fourier %D 2020 %P 1029-1084 %V 70 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3330/ %R 10.5802/aif.3330 %G en %F AIF_2020__70_3_1029_0
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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