The deficiencies of Kaehler groups

Abstract

Generalizing the theorem of Green--Lazarsfeld and Gromov, we classify Kaehler groups of deficiency at least two. As a consequence we see that there are no Kaehler groups of even and strictly positive deficiency. With the same arguments we prove that Kaehler groups that are non-Abelian and are limit groups in the sense of Sela are surface groups.

10 pages; small edits in v2; corrected a type on v3; to appear in Journal of Topology

References in corpus (2)

• On pseudo-harmonic maps in conformal geometry
• Low dimensional projective groups

Cited by in corpus (7)

• Kähler groups and subdirect products of surface groups
• Coxeter groups and Kähler groups
• Presentability by products for some classes of groups
• Complex hypersurfaces in direct products of Riemann surfaces
• Finite groups of arbitrary deficiency
• Sasaki versus Kähler groups
• Restrictions on the prime to $p$ fundamental group of a smooth projective variety