Which 3-manifold groups are Kähler groups?

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).

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

References in corpus (3)

• Ricci flow with surgery on three-manifolds
• Ricci Flow and the Poincare Conjecture
• Boundary manifolds of projective hypersurfaces

Cited by in corpus (13)

• Topology and geometry of cohomology jump loci
• Geometric and algebraic aspects of 1-formality
• Fundamental groups, Alexander invariants, and cohomology jumping loci
• Quasi-Kähler groups, 3-manifold groups, and formality
• Abelian duality and propagation of resonance
• Kähler groups and subdirect products of surface groups
• Three-manifolds and Kaehler groups
• Quasiprojective three-manifold groups and complexification of three-manifolds
• Kaehlerian three-manifold groups
• Three manifold groups, Kaehler groups and complex surfaces
• Cohomology jump loci of 3-manifolds
• Poincaré duality and resonance varieties
• Solving the isomorphism problems for two families of parafree groups