Partial periodic quotients of groups acting on a hyperbolic space

Coulon, Rémi B.

Annales de l'Institut Fourier, Tome 66 (2016) no. 5, pp. 1773-1857.

Dans cet article, nous construisons des quotients partiellement périodiques de groupes admettant une action acylindrique sur un espace hyperbolique. En particulier, nous produisons des quotients infinis de groupes modulaires de surfaces, dans lesquelles une puissance fixée de tout homéomorphisme s’identifie avec un élément réductible ou un élément d’ordre fini.

In this article, we construct partial periodic quotients of groups which have a non-elementary acylindrical action on a hyperbolic space. In particular, we provide infinite quotients of mapping class groups where a fixed power of every homeomorphism is identified with a periodic or reducible element.

Classification : 10X99, 14A12, 11L05
Keywords: Small cancellation theory, mapping class groups, hyperbolic spaces, periodic quotients
Mot clés : géométrie hyperbolique, groupes périodiques, théorie de la petite simplification, action acylindrique, groupe modulaire de surface.

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