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Cubulable Kähler
groups
Thomas Delzant and Pierre Py |
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Geometry & Topology 23 (2019) 2125–2164
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Abstract |
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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. |
Keywords
Kähler manifolds, cubical complexes
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Mathematical Subject Classification 2010
Primary: 20F65, 32Q15
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References |
Publication
Received: 20 February 2018
Revised: 23 October 2018
Accepted: 2 December 2018
Published: 17 June 2019
Proposed: Jean-Pierre Otal
Seconded: Martin Bridson, Benson Farb
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Authors |
| Thomas Delzant | |
| IRMA Université de Strasbourg CNRS Strasbourg France |
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| Pierre Py | |
| Instituto de Matemáticas Universidad Nacional Autónoma de México Ciudad Universitaria Ciudad de México Mexico |
IRMA Université de Strasbourg CNRS Strasbourg France |
