Dense embeddings of surface groups. (English) Zbl 1132.22011
Summary: 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.
MSC:
| 22E40 | Discrete subgroups of Lie groups |
| 22E15 | General properties and structure of real Lie groups |
| 20H10 | Fuchsian groups and their generalizations (group-theoretic aspects) |
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