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Compactifications and algebraic completions of limit groups

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Abstract

This paper considers the existence of nondiscrete embeddings Γ ↦ G, where Γ is an abstract limit group and G is topological group. Namely, it is shown that a locally compact group G that admits a nondiscrete nonabelian free subgroup F admits a nondiscrete copy of every nonabelian limit group L. In some cases, for instance if the F is of rank 2 and its closure in G is compact or semisimple algebraic, or if L is a surface group (as considered in [6]), L can be chosen with the same closure as F.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, 1 Oxford ST, Cambridge, MA, 02138, USA

    Jonathan Barlev

  2. Einstein Institute of Mathematics, Hebrew University of Jerusalem, Givat-Ram, Jerusalem, 91904, Israel

    Tsachik Gelander

Authors
  1. Jonathan Barlev
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  2. Tsachik Gelander
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Correspondence to Jonathan Barlev.

Additional information

T. Gelander acknowledges financial support from the European Community’s seventh Framework Programme (FP7/2007-2013)/ERC grant agreement 260508, and from the Israeli Science Foundation.

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Barlev, J., Gelander, T. Compactifications and algebraic completions of limit groups. JAMA 112, 261–287 (2010). https://doi.org/10.1007/s11854-010-0030-3

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  • DOI: https://doi.org/10.1007/s11854-010-0030-3

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