Character varieties of virtually nilpotent Kähler groups and G–Higgs bundles
Annales de l'Institut Fourier, Volume 65 (2015) no. 6, pp. 2601-2612.

Let G be a connected complex reductive affine algebraic group, and let KG be a maximal compact subgroup. Let X be a compact connected Kähler manifold whose fundamental group Γ is virtually nilpotent. We prove that the character variety Hom(Γ,G)//G admits a natural strong deformation retraction to the subset Hom(Γ,K)/KHom(Γ,G)//G. The natural action of * on the moduli space of G–Higgs bundles over X extends to an action of . This produces the above mentioned deformation retraction.

Soit G un groupe algébrique affine réductif complexe connexe, et soit KG un sous-groupe compact maximal. Soit X une variété Kählerienne compacte connexe dont le groupe fondamental Γ est virtuellement nilpotent. Nous montrons que la variété de caractères Hom(Γ,G)//G admet une rétraction par déformation forte naturelle sur le sous-ensemble Hom(Γ,K)/KHom(Γ,G)//G. L’action naturelle de * sur l’espace des modules de G-fibrés de Higgs sur X s’étend à une action de . Ceci produit la rétraction par déformation mentionnée ci-dessus.

DOI: 10.5802/aif.2997
Classification: 20G20, 14J60
Keywords: Kähler group, character variety, $G$–Higgs bundle, virtually nilpotent group
Mot clés : Groupes de Kähler, variété des caractères, $G$-fibrés de Higgs, groupe virtuellement nilpotent
Biswas, Indranil 1; Florentino, Carlos 2

1 School of Mathematics Tata Institute of Fundamental Research, Homi Bhabha Road Bombay 400005 (India)
2 Departamento Matemática Instituto Superior Técnico Av. Rovisco Pais 1049-001 Lisbon (Portugal)
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Biswas, Indranil; Florentino, Carlos. Character varieties of virtually nilpotent Kähler groups and $G$–Higgs bundles. Annales de l'Institut Fourier, Volume 65 (2015) no. 6, pp. 2601-2612. doi : 10.5802/aif.2997. http://www.numdam.org/articles/10.5802/aif.2997/

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