Which 3-manifold groups are Kähler groups?

Details Which 3-manifold groups are Kähler groups? Which 3-manifold groups are Kähler groups?

2007-09-27

arxiv.org/abs/0709.4350v2

Journal of the European Mathematical Society 11 (2009), no. 3, 521-528

Mathematics

Algebraic Geometry

8 pages, accepted for publication in the Journal of the European Mathematical Society

Scientific paper

10.4171/JEMS/158

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 K\"ahler manifold, then G must be finite, and thus belongs to the
well-known list of finite subgroups of O(4).

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