[Espaces homogènes complexes conjugués avec groupes fondamentaux non isomorphes]
Soit le quotient d'un C-groupe algébrique réductif connexe G par un sous-groupe fini Γ. On décrit le groupe fondamental topologique de l'espace homogène X, qui est non abélien quand Γ est non abélien. Puis on construit un exemple d'espace homogène X et d'automorphisme σ de C tels que les groupes fondamentaux topologiques de X et de la variété conjuguée σX ne sont pas isomorphes.
Let be the quotient of a connected reductive algebraic C-group G by a finite subgroup Γ. We describe the topological fundamental group of the homogeneous space X, which is nonabelian when Γ is nonabelian. Further, we construct an example of a homogeneous space X and an automorphism σ of C such that the topological fundamental groups of X and of the conjugate variety σX are not isomorphic.
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@article{CRMATH_2015__353_11_1001_0,
author = {Borovoi, Mikhail and Cornulier, Yves},
title = {Conjugate complex homogeneous spaces with non-isomorphic fundamental groups},
journal = {Comptes Rendus. Math\'ematique},
pages = {1001--1005},
publisher = {Elsevier},
volume = {353},
number = {11},
year = {2015},
doi = {10.1016/j.crma.2015.09.010},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.09.010/}
}
TY - JOUR AU - Borovoi, Mikhail AU - Cornulier, Yves TI - Conjugate complex homogeneous spaces with non-isomorphic fundamental groups JO - Comptes Rendus. Mathématique PY - 2015 SP - 1001 EP - 1005 VL - 353 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.09.010/ DO - 10.1016/j.crma.2015.09.010 LA - en ID - CRMATH_2015__353_11_1001_0 ER -
%0 Journal Article %A Borovoi, Mikhail %A Cornulier, Yves %T Conjugate complex homogeneous spaces with non-isomorphic fundamental groups %J Comptes Rendus. Mathématique %D 2015 %P 1001-1005 %V 353 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.09.010/ %R 10.1016/j.crma.2015.09.010 %G en %F CRMATH_2015__353_11_1001_0
Borovoi, Mikhail; Cornulier, Yves. Conjugate complex homogeneous spaces with non-isomorphic fundamental groups. Comptes Rendus. Mathématique, Tome 353 (2015) no. 11, pp. 1001-1005. doi : 10.1016/j.crma.2015.09.010. http://www.numdam.org/articles/10.1016/j.crma.2015.09.010/
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