Three-manifolds and Kaehler groups

Abstract

We give a simple proof of a result originally due to Dimca and Suciu: a group that is both Kaehler and the fundamental group of a closed three-manifold is finite. We also prove that a group that is both the fundamental group of a closed three-manifold and of a non-Kaehler compact complex surface is infinite cyclic or the direct product of an infinite cyclic group and a group of order two.

6 pages; corrected statement of Theorem 6; final version to appear in Ann. Inst. Fourier

References in corpus (3)

• Ricci flow with surgery on three-manifolds
• Which 3-manifold groups are Kähler groups?
• Kaehler groups and duality

Cited by in corpus (6)

• Kähler groups and subdirect products of surface groups
• Quasiprojective three-manifold groups and complexification of three-manifolds
• Kaehlerian three-manifold groups
• Low dimensional projective groups
• On the fundamental groups of compact Sasakian manifolds
• Sasaki versus Kähler groups