Compactifications and algebraic completions of limit groups

Jonathan Barlev; Tsachik Gelander

doi:10.1007/s11854-010-0030-3

Compactifications and algebraic completions of limit groups

Jonathan Barlev^*, Tsachik Gelander

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

This paper considers the existence of nondiscrete embeddings Γ {mapping} 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.

Original language	English (US)
Pages (from-to)	261-287
Number of pages	27
Journal	Journal d'Analyse Mathematique
Volume	112
Issue number	1
DOIs	https://doi.org/10.1007/s11854-010-0030-3
State	Published - 2010

Funding

∗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.

ASJC Scopus subject areas

Analysis
General Mathematics

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AB - This paper considers the existence of nondiscrete embeddings Γ {mapping} 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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Compactifications and algebraic completions of limit groups

Abstract

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