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Zbl pre05565389
Dimca, Alexandru; Suciu, Alexander I.
Which 3-manifold groups are Kähler groups? (English)
[J] J. Eur. Math. Soc. (JEMS) 11, No. 3, 521-528 (2009). ISSN 1435-9855; ISSN 1435-9863

Summary: The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if $G$ can be realized as both the fundamental group of a closed 3-manifold and of a compact Kähler manifold, then $G$ must be finite-and thus belongs to the well-known list of finite subgroups of O(4), acting freely on $S^{3}$.

MSC 2000:: *20F34 Fundamental groups and their automorphisms
32J27 Compact Kähler manifolds
57N10 Topology of general 3-manifolds
14F35 Homotopy theory (algebraic geometry)
55N25 Homology with local coefficients, equivariant cohomology

Keywords: Kähler manifold; 3-manifold; fundamental group; cohomology ring; resonance variety; isotropic subspace

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