Compact Connected Components In Relative Character Varieties Of Punctured Spheres
Résumé
We prove that some relative character varieties of the fundamental group of a punctured sphere into the Hermitian Lie groups SU(p, q) admit compact connected components. The representations in these components have several counter-intuitive properties. For instance, the image of any simple closed curve is an elliptic element. These results extend a recent work of Deroin and the first author, which treated the case of PU(1, 1) = PSL(2, R). Our proof relies on the non-Abelian Hodge correspondance between relative character varieties and parabolic Higgs bundles. The examples we construct admit a rather explicit description as projective varieties obtained via Geometric Invariant Theory.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
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