Limit groups as limits of free groups: compactifying the set of free groups
Abstract
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 marked groups. Many results get a natural interpretation in this setting. The class of limit groups is known to coincide with the class of finitely generated fully residually free groups. The topological approach gives some new insight on the relation between fully residually free groups, the universal theory of free groups, ultraproducts and nonstandard free groups.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2004
 arXiv:
 arXiv:math/0401042
 Bibcode:
 2004math......1042C
 Keywords:

 Mathematics  Group Theory
 EPrint:
 Decembre 2003. 57 pages. (Correction d'une imprecision)