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arXiv · 1505.02323

Conjugate complex homogeneous spaces with non-isomorphic fundamental groups

Mikhail Borovoi·Yves Cornulier
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Abstract

Let X=G/H be the quotient of a connected reductive algebraic C-group G defined over the field of complex numbers C by a finite subgroup H. We describe the topological fundamental group of the homogeneous space X, which is nonabelian when H is nonabelian. Further, we construct an example of a homogeneous space X and an automorphism s of C such that the topological fundamental groups of X and of the conjugate variety sX are not isomorphic.

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Mikhail Borovoi, Yves Cornulier. 2015-05-09. Conjugate complex homogeneous spaces with non-isomorphic fundamental groups. https://doi.org/10.1016/j.crma.2015.09.010

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