Three-manifolds and Kähler groups

[Variétés trois-dimensionelles et groupes de Kähler]

Kotschick, D.

Annales de l'Institut Fourier, Tome 62 (2012), p. 1081-1090 / Harvested from Numdam

Résumé

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 $\mathbb{ Z}$ soit $\mathbb{ Z}\oplus \mathbb{ Z}_2$.

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 $\mathbb{ Z}\oplus \mathbb{ Z}_2$.

Détail

Publié le : 2012-01-01

MR 3013817 | Zbl 1275.32018

DOI : https://doi.org/10.5802/aif.2717
Classification:  32Q15,  57M05,  14F35,  32J15,  57M50
Mots clés: groupes fondamentaux des variétés trois-dimensionelles, groupes de Kähler

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