JournalsjemsVol. 11 , No. 3DOI 10.4171/jems/158

Which 3-manifold groups are Kähler groups?

  • Alexander I. Suciu

    Northeastern University, Boston, USA
  • Alexandru Dimca

    Université de Nice Sophia Antipolis, France
Which 3-manifold groups are Kähler groups? cover

Abstract

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.