Geometry & Topology
- Geom. Topol.
- Volume 23, Number 4 (2019), 2125-2164.
Cubulable Kähler groups
We prove that a Kähler group which is cubulable, i.e. which acts properly discontinuously and cocompactly on a 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 cubical complexes, under the assumption that there is no fixed point in the visual boundary.
Geom. Topol., Volume 23, Number 4 (2019), 2125-2164.
Received: 20 February 2018
Revised: 23 October 2018
Accepted: 2 December 2018
First available in Project Euclid: 16 July 2019
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Delzant, Thomas; Py, Pierre. Cubulable Kähler groups. Geom. Topol. 23 (2019), no. 4, 2125--2164. doi:10.2140/gt.2019.23.2125. https://projecteuclid.org/euclid.gt/1563242526