Character varieties; Homotopy; Bad representations; singularities; free group
Résumé :
[en] Let G be a connected, reductive, complex affine algebraic group, and let Xr denote the moduli space of G-valued representations of a rank r free group. We first characterize the singularities in Xr resolving conjectures of Florentino-Lawton. In particular, we compute the codimension of the orbifold singular locus using facts about Borel-de Siebenthal groups. We then use this codimension to calculate some higher homotopy groups of the smooth locus of Xr, proving conjectures of Florentino-Lawton-Ramras. Lastly, using the earlier analysis of Borel-de Siebenthal groups, we prove a conjecture of Sikora about CI Lie groups.
Disciplines :
Mathématiques
Auteur, co-auteur :
GUERIN, Clément ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Lawton, Sean; George Mason University > Mathematics > Associate Professor
Ramras, Daniel; Indiana University-Purdue University Indianapolis > Mathematics > Associate Professor
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Bad representations and homotopy groups of Character Varieties
Titre traduit :
[fr] Représentations exceptionnelles et groupe d'homotopie des variétés de caractères
Date de publication/diffusion :
2022
Titre du périodique :
Annales Henri Lebesgue
Volume/Tome :
5
Pagination :
93-140
Peer reviewed :
Peer reviewed
Projet FnR :
FNR11405402 - Analysis And Geometry Of Low-dimensional Manifolds, 2016 (01/09/2017-28/02/2021) - Jean-marc Schlenker
