Three-manifolds and Kähler groups

D. Kotschick[1]

  • [1] Mathematisches Institut, LMU München, Theresienstr. 39, 80333 München, Germany

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 3, page 1081-1090
  • ISSN: 0373-0956

Abstract

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We give a simple proof of a result originally due to Dimca and Suciu: a group that is both Kähler and the fundamental group of a closed three-manifold is finite. We also prove that a group that is both the fundamental group of a closed three-manifold and of a non-Kähler compact complex surface is ℤ or ℤ ⊕ ℤ 2 .

How to cite

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Kotschick, D.. "Three-manifolds and Kähler groups." Annales de l’institut Fourier 62.3 (2012): 1081-1090. <http://eudml.org/doc/251121>.

@article{Kotschick2012,
abstract = {We give a simple proof of a result originally due to Dimca and Suciu: a group that is both Kähler and the fundamental group of a closed three-manifold is finite. We also prove that a group that is both the fundamental group of a closed three-manifold and of a non-Kähler compact complex surface is $\mathbb\{ Z\}$ or $\mathbb\{ Z\}\oplus \mathbb\{ Z\}_2$.},
affiliation = {Mathematisches Institut, LMU München, Theresienstr. 39, 80333 München, Germany},
author = {Kotschick, D.},
journal = {Annales de l’institut Fourier},
keywords = {three-manifold groups; Kähler groups},
language = {eng},
number = {3},
pages = {1081-1090},
publisher = {Association des Annales de l’institut Fourier},
title = {Three-manifolds and Kähler groups},
url = {http://eudml.org/doc/251121},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Kotschick, D.
TI - Three-manifolds and Kähler groups
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 3
SP - 1081
EP - 1090
AB - We give a simple proof of a result originally due to Dimca and Suciu: a group that is both Kähler and the fundamental group of a closed three-manifold is finite. We also prove that a group that is both the fundamental group of a closed three-manifold and of a non-Kähler compact complex surface is $\mathbb{ Z}$ or $\mathbb{ Z}\oplus \mathbb{ Z}_2$.
LA - eng
KW - three-manifold groups; Kähler groups
UR - http://eudml.org/doc/251121
ER -

References

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