Branched covers of elliptic curves and Kähler groups with exotic finiteness properties
[Revêtements ramifiés de courbes elliptiques et groupes kähleriens avec propriétés de finitude exotiques]
Annales de l'Institut Fourier, Tome 69 (2019) no. 1, pp. 335-363.

Nous construisons des groupes kähleriens ayant des propriétés de finitude arbitraires en considérant des applications holomorphes de produits de surfaces de Riemann vers une courbe elliptique : pour tout r3, nous obtenons une grande classe de groupes kähleriens qui ont un espace classifiant avec un (r-1)-squelette fini, mais n’ont aucun espace classifiant avec un nombre fini de r-cellules. Nous décrivons des invariants qui distinguent beaucoup de ces groupes. Notre construction est inspirée par les exemples de Dimca, Papadima et Suciu.

We construct Kähler groups with arbitrary finiteness properties by mapping products of closed Riemann surfaces holomorphically onto an elliptic curve: for each r3, we obtain large classes of Kähler groups that have classifying spaces with finite (r-1)-skeleton but do not have classifying spaces with finitely many r-cells. We describe invariants which distinguish many of these groups. Our construction is inspired by examples of Dimca, Papadima and Suciu.

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DOI : https://doi.org/10.5802/aif.3245
Classification : 32J27,  20J05,  20F65
Mots clés : Groupes kähleriens, propriétés de finitude homologiques, Revêtements ramifiés
@article{AIF_2019__69_1_335_0,
     author = {Llosa Isenrich, Claudio},
     title = {Branched covers of elliptic curves and K\"ahler groups with exotic finiteness properties},
     journal = {Annales de l'Institut Fourier},
     pages = {335--363},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {69},
     number = {1},
     year = {2019},
     doi = {10.5802/aif.3245},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.3245/}
}
Llosa Isenrich, Claudio. Branched covers of elliptic curves and Kähler groups with exotic finiteness properties. Annales de l'Institut Fourier, Tome 69 (2019) no. 1, pp. 335-363. doi : 10.5802/aif.3245. http://archive.numdam.org/articles/10.5802/aif.3245/

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