Comptes Rendus
no. 11
Algebraic geometry/Topology
Conjugate complex homogeneous spaces with non-isomorphic fundamental groups
Presented by: Jean-Pierre Serre
Mikhail Borovoi1; Yves Cornulier2
1 Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, 6997801 Tel Aviv, Israel
2 Laboratoire de mathématiques d'Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay cedex, France
Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1001-1005

Let X=G/Γ 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.

Soit X=G/Γ 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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.09.010
Keywords: Fundamental group, Conjugate variety, Homogeneous space, Linear algebraic group

Mikhail Borovoi 1; Yves Cornulier 2

1 Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, 6997801 Tel Aviv, Israel
2 Laboratoire de mathématiques d'Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay cedex, France 
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Mikhail Borovoi; Yves Cornulier. Conjugate complex homogeneous spaces with non-isomorphic fundamental groups. Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1001-1005. doi: 10.1016/j.crma.2015.09.010

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