Cubulable K\"ahler groups
Geometric Topology
2019-06-26 v1 Algebraic Geometry
Group Theory
Abstract
We prove that a K\"ahler 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 K\"ahler 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 K\"ahler groups on irreducible, locally finite CAT(0) cubical complexes, under the assumption that there is no fixed point in the visual boundary.
Cite
@article{arxiv.1609.08474,
title = {Cubulable K\"ahler groups},
author = {Thomas Delzant and Pierre Py},
journal= {arXiv preprint arXiv:1609.08474},
year = {2019}
}