Bad representations and homotopy groups of Character Varieties

Guerin, Clément; Lawton, Sean; Ramras, Daniel

Reference : Bad representations and homotopy groups of Character Varieties


	Document type :	E-prints/Working papers : Already available on another site
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/40086

Title :	Bad representations and homotopy groups of Character Varieties
Language :	English
Translated title :	[fr] Représentations exceptionnelles et groupe d'homotopie des variétés de caractères
Author, co-author :	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]
Publication date :	8-Aug-2019
Edition :	1
Number of pages :	38
Peer reviewed :	No
Keywords :	[en] Character varieties ; Homotopy ; Bad representations ; singularities ; free group
Abstract :	[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.
Permalink :	http://hdl.handle.net/10993/40086
source URL :	https://arxiv.org/abs/1908.02915
FnR project :	FnR ; FNR11405402 > Jean-Marc Schlenker > AGoLoM > Analysis and Geometry of Low-dimensional Manifolds > 01/09/2017 > 31/08/2020 > 2016

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