曲面群的稠密嵌入
Dense embeddings of surface groups
摘要：
讨论了曲面群和全剩余自由群在拓扑群中的稠密嵌入。证明了一个紧拓扑群包含一个有限秩的非交换稠密自由群当且仅当它包含一个稠密曲面群。同时，我们还得到了那些允许一个稠密忠实嵌入曲面群的李群的一个特征。同样，我们证明了任何连通半单李群都包含任何完全剩余自由群的稠密副本。
英文摘要：
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.
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