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.

Locations

• arXiv (Cornell University) - View - PDF
• Project Euclid (Cornell University) - View - PDF
• DataCite API - View
• Geometry & Topology - View - PDF