## Geometry & Topology

### Dense embeddings of surface groups

#### 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.

#### Article information

Source
Geom. Topol., Volume 10, Number 3 (2006), 1373-1389.

Dates
Revised: 3 August 2006
Accepted: 18 June 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513799770

Digital Object Identifier
doi:10.2140/gt.2006.10.1373

Mathematical Reviews number (MathSciNet)
MR2255501

Zentralblatt MATH identifier
1132.22011

#### Citation

Breuillard, Emmanuel; Gelander, Tsachik; Souto, Juan; Storm, Peter. Dense embeddings of surface groups. Geom. Topol. 10 (2006), no. 3, 1373--1389. doi:10.2140/gt.2006.10.1373. https://projecteuclid.org/euclid.gt/1513799770

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