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.
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.
Revised:
Accepted:
Published online:
Classification: 20G20, 14J60
Keywords: Kähler group, character variety, –Higgs bundle, virtually nilpotent group
@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/} }
TY - JOUR TI - Character varieties of virtually nilpotent Kähler groups and $G$–Higgs bundles JO - Annales de l'Institut Fourier PY - 2015 DA - 2015/// SP - 2601 EP - 2612 VL - 65 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2997/ UR - https://doi.org/10.5802/aif.2997 DO - 10.5802/aif.2997 LA - en ID - AIF_2015__65_6_2601_0 ER -
%0 Journal Article %T Character varieties of virtually nilpotent Kähler groups and $G$–Higgs bundles %J Annales de l'Institut Fourier %D 2015 %P 2601-2612 %V 65 %N 6 %I Association des Annales de l’institut Fourier %U https://doi.org/10.5802/aif.2997 %R 10.5802/aif.2997 %G en %F 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, Volume 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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