Local coordinates for SL(n,C)-character varieties of finite-volume hyperbolic 3-manifolds
[Coordonnées locales pour la variété des SL(n,C)-caractères des 3-variétés hyperboliques à volume fini]
Annales Mathématiques Blaise Pascal, Tome 19 (2012) no. 1, pp. 107-122.

Étant donnée une 3-variété hyperbolique à volume fini, on compose un relevé dans SL(2,C) de son holnomie avec la représentation irreductible et n-dimensionnelle de SL(2,C) dans SL(n,C). Dans cet article on donne des coordonnées locales autour du caractère de cette représentation. Comme corollaire, cette representation est isolée parmi toutes les représentations qui sont unipotentes aux bouts.

Given a finite-volume hyperbolic 3-manifold, we compose a lift of the holonomy in SL(2,C) with the n-dimensional irreducible representation of SL(2,C) in SL(n,C). In this paper we give local coordinates of the SL(n,C)-character variety around the character of this representation. As a corollary, this representation is isolated among all representations that are unipotent at the cusps.

DOI : https://doi.org/10.5802/ambp.306
Classification : 53C24,  57M50,  20C15
Mots clés: rigidité infinitesimale, variété des caractères, 3-variété hyperbolique, cohomolgie L2
@article{AMBP_2012__19_1_107_0,
     author = {Pere Menal-Ferrer and Joan Porti},
     title = {Local coordinates for $\operatorname{SL}(n,\mathbf{C})$-character varieties of finite-volume hyperbolic 3-manifolds},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {107--122},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {19},
     number = {1},
     year = {2012},
     doi = {10.5802/ambp.306},
     mrnumber = {2978315},
     zbl = {1252.53053},
     language = {en},
     url = {ambp.centre-mersenne.org/item/AMBP_2012__19_1_107_0/}
}
Pere Menal-Ferrer; Joan Porti. Local coordinates for $\operatorname{SL}(n,\mathbf{C})$-character varieties of finite-volume hyperbolic 3-manifolds. Annales Mathématiques Blaise Pascal, Tome 19 (2012) no. 1, pp. 107-122. doi : 10.5802/ambp.306. https://ambp.centre-mersenne.org/item/AMBP_2012__19_1_107_0/

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