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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The space of geometric limits of one-generator closed subgroups of $\mathrm{PSL}_2(\mathbb{R})$

Hyungryul Baik and Lucien Clavier

Algebraic & Geometric Topology 13 (2013) 549–576
Abstract

We give a complete description of the closure of the space of one-generator closed subgroups of PSL2() for the Chabauty topology, by computing explicitly the matrices associated with elements of Aut(D)PSL2(), and finding quantities parametrizing the limit cases. Along the way, we investigate under what conditions sequences of maps φn: X Y transform convergent sequences of closed subsets of the domain X into convergent sequences of closed subsets of the range Y . In particular, this allows us to compute certain geometric limits of PSL2() only by looking at the Hausdorff limit of some closed subsets of .

Keywords
PSL2(R), Chabauty topology, Hausdorff topology, geometric limit
Mathematical Subject Classification 2010
Primary: 30F40
Secondary: 20H10
References
Publication
Received: 24 February 2012
Revised: 18 July 2012
Accepted: 4 October 2013
Published: 10 March 2013
Authors
Hyungryul Baik
Department of Mathematics
Cornell University
310 Malott Hall
Ithaca
New York 14853-4201
USA
http://www.math.cornell.edu/~hrbaik/
Lucien Clavier
Department of Mathematics
Cornell University
310 Malott Hall
Ithaca
New York 14853-4201
USA
http://www.math.cornell.edu/~lpc49/