Three-manifolds and Kähler groups
Annales de l'Institut Fourier, Volume 62 (2012) no. 3, p. 1081-1090

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 or 2 .

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 soit 2 .

DOI : https://doi.org/10.5802/aif.2717
Classification:  32Q15,  57M05,  14F35,  32J15,  57M50
Keywords: three-manifold groups, Kähler groups
@article{AIF_2012__62_3_1081_0,
     author = {Kotschick, D.},
     title = {Three-manifolds and K\"ahler groups},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {62},
     number = {3},
     year = {2012},
     pages = {1081-1090},
     doi = {10.5802/aif.2717},
     mrnumber = {3013817},
     zbl = {1275.32018},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2012__62_3_1081_0}
}
Kotschick, D. Three-manifolds and Kähler groups. Annales de l'Institut Fourier, Volume 62 (2012) no. 3, pp. 1081-1090. doi : 10.5802/aif.2717. http://www.numdam.org/item/AIF_2012__62_3_1081_0/

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