2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221823We 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.This is the version published by Geometry & Topology on 4 October 2006Group TheoryGeometric Topology22E40, 20H10text