Compactifications and algebraic completions of Limit groups

Details Compactifications and algebraic completions of Limit groups Compactifications and algebraic completions of Limit groups

2009-04-24

arxiv.org/abs/0904.3771v3

Journal D'Analyse Mathematique Volume 112 (2010), Number 1, 261-287

Mathematics

Group Theory

v2: Substantial changes to sections 7 and 8.2. Typos corrected. References added. v3: Acknowledgement corrected

Scientific paper

10.1007/s11854-010-0030-3

In this paper we consider the existence of dense embeddings of Limit groups in locally compact groups generalizing earlier work of Breuillard, Gelander, Souto and Storm [GBSS] where surface groups were considered. Our main results are proved in the context of compact groups and algebraic groups over local fields. In addition we prove a generalization of the classical Baumslag lemma which is a useful tool for generating eventually faithful sequences of homomorphisms. The last section is dedicated to correct a mistake from [BGSS] and to get rid of the even genus assumption.

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