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

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

2004-01-06

arxiv.org/abs/math/0401042v2

Isra\"{e}l Journal of Mathematics 146 (2005) 1

Mathematics

Group Theory

Decembre 2003. 57 pages. (Correction d'une imprecision)

Scientific paper

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 non-standard free groups.

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