Cubulable Kähler groups

Abstract

We prove that a Kähler group which is cubulable, i.e. which acts properly discontinuously and cocompactly on a CAT(0) cubical complex, has a finite index subgroup isomorphic to a direct product of surface groups, possibly with a free Abelian factor. Similarly, we prove that a closed aspherical Kähler manifold with a cubulable fundamental group has a finite cover which is biholomorphic to a topologically trivial principal torus bundle over a product of Riemann surfaces. Along the way, we prove a factorization result for essential actions of Kähler groups on irreducible, locally finite CAT(0) cubical complexes, under the assumption that there is no fixed point in the visual boundary.

References in corpus (1)

• Non-finiteness properties of fundamental groups of smooth projective varieties

Cited by in corpus (5)

• Cross ratios and cubulations of hyperbolic groups
• Kähler groups and subdirect products of surface groups
• Mapping class groups, multiple Kodaira fibrations, and CAT(0) spaces
• Complex hypersurfaces in direct products of Riemann surfaces
• Relatively geometric actions of Kähler groups on CAT(0) cube complexes