Kaehlerian three-manifold groups

TL;DR

This paper proves that the fundamental group of any three-manifold that is a Kaehler group must be either finite or correspond to a closed orientable surface, regardless of manifold's orientability or compactness.

Contribution

It establishes a classification of three-manifold groups that are Kaehler, extending previous results to non-closed and non-orientable cases.

Findings

Kaehler three-manifold groups are either finite or surface groups

The result applies to non-closed and non-orientable three-manifolds

Provides a complete classification of such groups

Abstract

We prove that if the fundamental group of an arbitrary three-manifold -- not necessarily closed, nor orientable -- is a Kaehler group, then it is either finite or the fundamental group of a closed orientable surface.