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Dense embeddings of
surface groups
Emmanuel Breuillard, Tsachik Gelander, Juan Souto and Peter Storm |
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Geometry & Topology 10 (2006) 1373–1389
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arXiv: math.GR/0602635 |
Abstract |
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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. |
Keywords
surface group, topological group, fully residually free
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Mathematical Subject Classification 2000
Primary: 22E40
Secondary: 20H10
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References |
Forward citations |
Publication
Received: 10 February 2006
Revised: 3 August 2006
Accepted: 18 June 2006
Published: 4 October 2006
Proposed: Benson Farb
Seconded: Jean-Pierre Otal, Walter Neumann
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Authors |
| Emmanuel Breuillard | |
| Université de Lille UFR de Mathematiques 59655 Villeneuve d’Ascq FRANCE |
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| Tsachik Gelander | |
| Mathematics Department Yale University 10 Hillhouse ave New Haven CT 06511 USA |
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| Juan Souto | |
| Dept of Maths University of Chicago 5734 S. University Avenue Chicago, IL 60637 USA |
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| Peter Storm | |
| Stanford University Mathematics, Bldg. 380 450 Serra Mall Stanford, CA 94305 USA |
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