Limit groups as limits of free groups: compactifying the set of free groups.

Christophe Champetier (1) , Vincent Guirardel (2)

1 IF - Institut Fourier
2 LEP - Laboratoire Émile Picard

We give a topological framework for the study of Sela's limit groups:limit groups are limits of free groups in a compact space of markedgroups.Many results get a natural interpretation in this setting.The class of limit groups is known to coincide with the class offinitely generated fully residually free groups.The topological approach gives some new insight on the relation betweenfully residually free groups, the universal theory of free groups,ultraproducts and non-standard free groups.

Mots clés: universal theory.; Limit groups; free groups; universal theory

Domaines: Théorie des groupes [math.GR]

Christophe Champetier, Vincent Guirardel. Limit groups as limits of free groups: compactifying the set of free groups.. Israel Journal of Mathematics, 2005, 146, pp.1. ⟨hal-00000980v3⟩