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Limit groups as limits of free groups

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Abstract

We give a topological framework for the study of Sela'slimit 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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Authors and Affiliations

  1. Institut Fourier, B.P. 74, 38402, Saint-Martin d'Hères, France

    Christophe Champetier

  2. Laboratoire E. Picard, UMR 5580, Bât 1R2, Université Paul Sabatier, 118 rte de Narbonne, 31062, Toulouse cedex 4, France

    Vincent Guirardel

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  1. Christophe Champetier
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  2. Vincent Guirardel
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Correspondence to Christophe Champetier.

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Champetier, C., Guirardel, V. Limit groups as limits of free groups. Isr. J. Math. 146, 1–75 (2005). https://doi.org/10.1007/BF02773526

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