[Composantes exotiques des variétés de représentations du groupe fondamental d'une surface dans SO(p,q) et les fibrés de Higgs correspondants]
Pour les groupes de Lie semisimples, les espaces de modules de fibrés de Higgs sur une surface de Riemann sont en correspondance avec les variétés de représentations du groupe fondamental de la surface. Pour de nombreux groupes, les invariants topologiques naturels distinguent les composantes connexes de l'espace des modules. Les représentations de Hitchin dans un groupe réel déployé et des représentations maximales dans un groupe hermitien fournissaient les seuls exemples connus jusqu'ici dans lesquels les invariants primitifs étaient insuffisants. Cette note a pour objet d'annoncer l'existence de nouvelles composantes exotiques pour les espaces de modules pour les groupes , pour .
For semisimple Lie groups, moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. In many cases, natural topological invariants label connected components of the moduli spaces. Hitchin representations into split real forms, and maximal representations into Hermitian Lie groups, are the only previously know cases where natural invariants do not fully distinguish connected components. In this note we announce the existence of new such exotic components in the moduli spaces for the groups with . These groups lie outside formerly know classes of groups associated with exotic components.
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@article{CRMATH_2018__356_6_666_0,
author = {Marta Aparicio-Arroyo and Steven Bradlow and Brian Collier and Oscar Garc{\'\i}a-Prada and Peter B. Gothen and Andr\'e Oliveira},
title = {Exotic components of {SO(\protect\emph{p},\protect\emph{q})} surface group representations, and their {Higgs} bundle avatars},
journal = {Comptes Rendus. Math\'ematique},
pages = {666--673},
publisher = {Elsevier},
volume = {356},
number = {6},
year = {2018},
doi = {10.1016/j.crma.2018.04.024},
language = {en},
}
TY - JOUR AU - Marta Aparicio-Arroyo AU - Steven Bradlow AU - Brian Collier AU - Oscar García-Prada AU - Peter B. Gothen AU - André Oliveira TI - Exotic components of SO(p,q) surface group representations, and their Higgs bundle avatars JO - Comptes Rendus. Mathématique PY - 2018 SP - 666 EP - 673 VL - 356 IS - 6 PB - Elsevier DO - 10.1016/j.crma.2018.04.024 LA - en ID - CRMATH_2018__356_6_666_0 ER -
%0 Journal Article %A Marta Aparicio-Arroyo %A Steven Bradlow %A Brian Collier %A Oscar García-Prada %A Peter B. Gothen %A André Oliveira %T Exotic components of SO(p,q) surface group representations, and their Higgs bundle avatars %J Comptes Rendus. Mathématique %D 2018 %P 666-673 %V 356 %N 6 %I Elsevier %R 10.1016/j.crma.2018.04.024 %G en %F CRMATH_2018__356_6_666_0
Marta Aparicio-Arroyo; Steven Bradlow; Brian Collier; Oscar García-Prada; Peter B. Gothen; André Oliveira. Exotic components of SO(p,q) surface group representations, and their Higgs bundle avatars. Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 666-673. doi : 10.1016/j.crma.2018.04.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.04.024/
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