[Coordonnées locales pour la variété des -caractères des 3-variétés hyperboliques à volume fini]
Given a finite-volume hyperbolic 3-manifold, we compose a lift of the holonomy in with the -dimensional irreducible representation of in . In this paper we give local coordinates of the -character variety around the character of this representation. As a corollary, this representation is isolated among all representations that are unipotent at the cusps.
Étant donnée une 3-variété hyperbolique à volume fini, on compose un relevé dans de son holnomie avec la représentation irreductible et -dimensionnelle de dans . 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.
Keywords: Infinitesimal Rigidity, Character Variety, Hyperbolic 3-Manifold, L2-Cohomology
Mots-clés : rigidité infinitesimale, variété des caractères, 3-variété hyperbolique, cohomolgie L2
Menal-Ferrer, Pere 1 ; Porti, Joan 1
@article{AMBP_2012__19_1_107_0,
author = {Menal-Ferrer, Pere and Porti, Joan},
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},
year = {2012},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {19},
number = {1},
doi = {10.5802/ambp.306},
zbl = {1252.53053},
mrnumber = {2978315},
language = {en},
url = {https://www.numdam.org/articles/10.5802/ambp.306/}
}
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Menal-Ferrer, Pere; Porti, Joan. 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
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