Journal of the European Mathematical Society

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Volume 11, Issue 3, 2009, pp. 521–528
DOI: 10.4171/JEMS/158

Published online: 2009-06-30

Which 3-manifold groups are Kähler groups?

Alexandru Dimca[1] and Alexander I. Suciu[2]

(1) Université de Nice Sophia Antipolis, France
(2) Northeastern University, Boston, USA

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 S3.

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

Dimca Alexandru, Suciu Alexander: Which 3-manifold groups are Kähler groups?. J. Eur. Math. Soc. 11 (2009), 521-528. doi: 10.4171/JEMS/158