Local coordinates for SL\((n,C)\)-character varieties of finite-volume hyperbolic 3-manifolds
type: Item
instance of: scholarly article
title: Local coordinates for SL\((n,C)\)-character varieties of finite-volume hyperbolic 3-manifolds
zbMATH Open document ID: 1252.53053
author: Pere Menal-Ferrer
author: Joan Porti
published in: Annales Mathématiques Blaise Pascal
publication date: 2012-08-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1111.4338
review text: Composing a lift of the holonomy of a finite-volume hyperbolic 3--manifold in \(SL(2,\mathbb C)\) with the \(n\)--dimensional irreducible representation of \(SL(2,\mathbb C)\) in \(SL(n,\mathbb C)\), the authors give local coordinates of the \(SL(n,\mathbb C)\)--character variety around the character of this representation. As a corollary, it is proved that this representation is isolated among all representations that are unipotent at the cusps.
reviewed by: Gheorghe Pitiş
Mathematics Subject Classification ID: 53C24
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 6065092
zbMATH Keywords: hyperbolic 3--manifold
zbMATH Keywords: character variety
zbMATH Keywords: \(L^2\)--cohomology
zbMATH Keywords: infinitesimal deformations
MaRDI profile type: Publication
OpenAlex ID: W2314877085
arXiv ID: 1111.4338
cites work: Q5393850
cites work: Rigidity of geometrically finite hyperbolic cone-manifolds
cites work: Hyperbolic manifolds and discrete groups
cites work: Varieties of representations of finitely generated groups
cites work: On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds
cites work: Twisted cohomology for hyperbolic three manifolds
cites work: On the First Cohomology of Discrete Subgroups of Semi-Simple Lie Groups
cites work: Remarks on the cohomology of groups
cites work: Local rigidity of 3-dimensional cone-manifolds
DOI: 10.5802/AMBP.306
description: scientific article; zbMATH DE number 6065092