Cubulable Kähler groups

Thomas Delzant; Pierre Py

doi:10.2140/gt.2019.23.2125

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arXiv · 1609.08474

Cubulable Kähler groups

Thomas Delzant·Pierre Py

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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.

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BibTeX RIS

Thomas Delzant, Pierre Py. 2016-09-27. Cubulable Kähler groups. https://doi.org/10.2140/gt.2019.23.2125

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