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Bulletin de la SMF - Parutions - 145 (2017) 193-223

Parutions < 145

Complexes of groups and geometric small cancelation over graphs of groups
Alexandre Martin
Bulletin de la SMF 145, fascicule 2 (2017), 193-223

Télécharger cet article : Fichier PDF

Résumé :
Complexes de groupes et petite simplification géométrique sur les graphes de groupes
Nous généralisons une construction de Gromov afin de réaliser certains groupes à petite simplification géométrique sur un graphe de groupes comme groupes fondamentaux de complexes de groupes de dimension 2 à courbure négative ou nulle. Nous donnons ensuite des conditions pour que l'hyperbolicité et certaines propriétés de finitude de tels groupes se déduisent des propriétés analogues pour les groupes locaux du graphe de groupes initial.

Mots-clefs : Petite simplification géométrique, complexes de groupes, groupes hyperboliques, espaces classifiants.

Abstract:
We explain and generalize a construction due to Gromov to realize geometric small cancelation groups over graphs of groups as fundamental groups of non-positively curved 2-dimensional complexes of groups. We then give conditions so that the hyperbolicity and some finiteness properties of the small cancelation quotient can be deduced from analogous properties for the local groups of the initial graph of groups.

Keywords: Geometric small cancelation, complexes of groups, hyperbolic groups, classifying spaces.

Class. math. : 20F65, 20E08, 57M07.


ISSN : 0037-9484
DOI : 10.24033/bsmf.2734
Publié avec le concours de : Centre National de la Recherche Scientifique

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