Geometry & Topology 10 (2006) 1373–1389

DOI: 10.2140/gt.2006.10.1373

arXiv: math.GR/0602635

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.

Keywords

surface group, topological group, fully residually free

Mathematical Subject Classification

Primary: 22E40

Secondary: 20H10

References

Publication

Received: 10 February 2006
Revised: 3 August 2006
Accepted: 18 June 2006
Published: 4 October 2006
Proposed: Benson Farb
Seconded: Jean-Pierre Otal, Walter Neumann

Authors