no. 6
Character varieties of virtually nilpotent Kähler groups and G–Higgs bundles
[Variétés de caractères des groupes de Kähler virtuellement nilpotents et G-fibrés de Higgs]
Annales de l'Institut Fourier, Tome 65 (2015) no. 6, pp. 2601-2612.

Soit G un groupe algébrique affine réductif complexe connexe, et soit K⊂G 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)/K⊂Hom(Γ,G)//G. L’action naturelle de ℂ * sur l’espace des modules de G-fibrés de Higgs sur X s’étend à une action de ℂ. Ceci produit la rétraction par déformation mentionnée ci-dessus.

Let G be a connected complex reductive affine algebraic group, and let K⊂G 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)/K⊂Hom(Γ,G)//G. The natural action of ℂ * on the moduli space of G–Higgs bundles over X extends to an action of ℂ. This produces the above mentioned deformation retraction.

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DOI : https://doi.org/10.5802/aif.2997
Classification : 20G20,  14J60
Mots clés : Groupes de Kähler, variété des caractères, G-fibrés de Higgs, groupe virtuellement nilpotent 
@article{AIF_2015__65_6_2601_0,
     author = {Biswas, Indranil and Florentino, Carlos},
     title = {Character varieties of virtually nilpotent {K\"ahler} groups and $G${{\textendash}Higgs} bundles},
     journal = {Annales de l'Institut Fourier},
     pages = {2601--2612},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {65},
     number = {6},
     year = {2015},
     doi = {10.5802/aif.2997},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2997/}
}
Biswas, Indranil; Florentino, Carlos. Character varieties of virtually nilpotent Kähler groups and $G$–Higgs bundles. Annales de l'Institut Fourier, Tome 65 (2015) no. 6, pp. 2601-2612. doi : 10.5802/aif.2997. https://aif.centre-mersenne.org/articles/10.5802/aif.2997/

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