Dense embeddings of surface groups

Details Dense embeddings of surface groups Dense embeddings of surface groups

2006-02-27

arxiv.org/abs/math/0602635v2

Geom. Topol. 10 (2006) 1373-1389

Mathematics

Group Theory

This is the version published by Geometry & Topology on 4 October 2006

Scientific paper

10.2140/gt.2006.10.1373

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.

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