Coxeter groups and Kähler groups

Abstract

We study homomorphisms from Kähler groups to Coxeter groups. As an application, we prove that a cocompact complex hyperbolic lattice (in complex dimension at least 2) does not embedd into a Coxeter group or a right-angled Artin group. This is in contrast with the case of real hyperbolic lattices.

10 pages, the proofs of the corollaries have been slightly simplified, the referee's comments have been included

References in corpus (2)

• The deficiencies of Kaehler groups
• One-relator Kaehler groups

Cited by in corpus (7)

• Kähler groups and subdirect products of surface groups
• Virtual algebraic fibrations of Kähler groups
• Cubulable Kähler groups
• Finite presentations for Kähler groups with arbitrary finiteness properties
• Cubulated hyperbolic groups admit Anosov representations
• Complex hypersurfaces in direct products of Riemann surfaces
• Les groupes de Burger-Mozes ne sont pas kählériens