no. 3
Three-manifolds and Kähler groups
[Variétés trois-dimensionelles et groupes de Kähler]
Kotschick, D.1
1 Mathematisches Institut, LMU München, Theresienstr. 39, 80333 München, Germany
Annales de l'Institut Fourier, Tome 62 (2012) no. 3, pp. 1081-1090.

On donne une preuve simple d’un résultat dû à Dimca et Suciu : un groupe de Kähler qui est aussi le groupe fondamental d’une variété trois-dimensionelle est fini. On montre également qu’un groupe qui est le groupe fondamental d’une variété trois-dimensionelle et en même temps le groupe fondamental d’une surface complexe compacte non-kählerienne est soit ℤ soit ℤ⊕ℤ 2 .

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 .

DOI : 10.5802/aif.2717
Classification : 32Q15, 57M05, 14F35, 32J15, 57M50
Keywords: three-manifold groups, Kähler groups
Mot clés : groupes fondamentaux des variétés trois-dimensionelles, groupes de Kähler

Kotschick, D. 1

1 Mathematisches Institut, LMU München, Theresienstr. 39, 80333 München, Germany 
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Kotschick, D. Three-manifolds and Kähler groups. Annales de l'Institut Fourier, Tome 62 (2012) no. 3, pp. 1081-1090. doi : 10.5802/aif.2717. https://aif.centre-mersenne.org/articles/10.5802/aif.2717/

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