Abstract
We discuss dense embeddings of surface groups and fully residually free groups in topological groups. We show that a compact topological group contains a nonabelian dense free group of finite rank if and only if it contains a dense surface group. Also, we obtain a characterization of those Lie groups which admit a dense faithfully embedded surface group. Similarly, we show that any connected semisimple Lie group contains a dense copy of any fully residually free group.
Citation
Emmanuel Breuillard. Tsachik Gelander. Juan Souto. Peter Storm. "Dense embeddings of surface groups." Geom. Topol. 10 (3) 1373 - 1389, 2006. https://doi.org/10.2140/gt.2006.10.1373
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