Soit un groupe algébrique affine réductif complexe connexe, et soit un sous-groupe compact maximal. Soit une variété Kählerienne compacte connexe dont le groupe fondamental est virtuellement nilpotent. Nous montrons que la variété de caractères admet une rétraction par déformation forte naturelle sur le sous-ensemble . L’action naturelle de sur l’espace des modules de -fibrés de Higgs sur s’étend à une action de . Ceci produit la rétraction par déformation mentionnée ci-dessus.
Let be a connected complex reductive affine algebraic group, and let be a maximal compact subgroup. Let be a compact connected Kähler manifold whose fundamental group is virtually nilpotent. We prove that the character variety admits a natural strong deformation retraction to the subset . The natural action of on the moduli space of –Higgs bundles over extends to an action of . This produces the above mentioned deformation retraction.
@article{AIF_2015__65_6_2601_0, author = {Biswas, Indranil and Florentino, Carlos}, title = {Character varieties of virtually nilpotent K\"ahler groups and $G$--Higgs bundles}, journal = {Annales de l'Institut Fourier}, volume = {65}, year = {2015}, pages = {2601-2612}, doi = {10.5802/aif.2997}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_2015__65_6_2601_0} }
Biswas, Indranil; Florentino, Carlos. Character varieties of virtually nilpotent Kähler groups and $G$–Higgs bundles. Annales de l'Institut Fourier, Tome 65 (2015) pp. 2601-2612. doi : 10.5802/aif.2997. http://gdmltest.u-ga.fr/item/AIF_2015__65_6_2601_0/
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