Reference : Bad representations and homotopy groups of Character Varieties
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/40086
Bad representations and homotopy groups of Character Varieties
English
[fr] Représentations exceptionnelles et groupe d'homotopie des variétés de caractères
Guerin, Clément mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Lawton, Sean mailto [George Mason University > Mathematics > Associate Professor]
Ramras, Daniel [Indiana University-Purdue University Indianapolis > Mathematics > Associate Professor]
8-Aug-2019
1
38
No
[en] Character varieties ; Homotopy ; Bad representations ; singularities ; free group
[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.
http://hdl.handle.net/10993/40086
https://arxiv.org/abs/1908.02915
FnR ; FNR11405402 > Jean-Marc Schlenker > AGoLoM > Analysis and Geometry of Low-dimensional Manifolds > 01/09/2017 > 31/08/2020 > 2016

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