Sur les automorphismes de groupes libres et de groupes de surface

Frédéric Paulin (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

The special linear groups, the mapping class groups of surfaces, the outer autormorphism groups of free groups appear in numerous domains. Their analogies, developped in particular in K.~Vogtmann's work, have been written about a lot. In this report, we concentrate on the contractible spaces on which these groups act in an analogous way, on the common properties of their subgroups, and on the similar (or conjecturally similar) properties of their asymptotic geometry.

Keywords: Automorphism group; free group; surface group; special linear group; group action on trees; Teichmüller space; Culler-Vogtmann's Outer space; asymptotic geometry of groups

Domains: Group Theory [math.GR]; Geometric Topology [math.GT]

Frédéric Paulin. Sur les automorphismes de groupes libres et de groupes de surface. 2010. ⟨hal-00628343⟩