TY - JOUR
T1 - Compactifications and algebraic completions of limit groups
AU - Barlev, Jonathan
AU - Gelander, Tsachik
N1 - Funding 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.
PY - 2010
Y1 - 2010
N2 - 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.
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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U2 - 10.1007/s11854-010-0030-3
DO - 10.1007/s11854-010-0030-3
M3 - Article
AN - SCOPUS:78651257756
SN - 0021-7670
VL - 112
SP - 261
EP - 287
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
IS - 1
ER -