Volume 10, issue 3 (2006)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Dense embeddings of surface groups

Emmanuel Breuillard, Tsachik Gelander, Juan Souto and Peter Storm

Geometry & Topology 10 (2006) 1373–1389

arXiv: math.GR/0602635

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.

Keywords
surface group, topological group, fully residually free
Mathematical Subject Classification 2000
Primary: 22E40
Secondary: 20H10
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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
Authors
Emmanuel Breuillard
Université de Lille
UFR de Mathematiques
59655 Villeneuve d’Ascq
FRANCE
Tsachik Gelander
Mathematics Department
Yale University
10 Hillhouse ave
New Haven CT 06511
USA
Juan Souto
Dept of Maths
University of Chicago
5734 S. University Avenue
Chicago, IL 60637
USA
Peter Storm
Stanford University
Mathematics, Bldg. 380
450 Serra Mall
Stanford, CA 94305
USA