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The space of geometric
limits of one-generator closed subgroups of
$\mathrm{PSL}_2(\mathbb{R})$
Hyungryul Baik and Lucien Clavier |
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Algebraic & Geometric Topology 13 (2013) 549–576
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Abstract |
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We give a complete description of the closure of the space of one-generator closed subgroups of for the Chabauty topology, by computing explicitly the matrices associated with elements of , and finding quantities parametrizing the limit cases. Along the way, we investigate under what conditions sequences of maps transform convergent sequences of closed subsets of the domain into convergent sequences of closed subsets of the range . In particular, this allows us to compute certain geometric limits of only by looking at the Hausdorff limit of some closed subsets of . |
Keywords
PSL2(R), Chabauty topology, Hausdorff topology, geometric
limit
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Mathematical Subject Classification 2010
Primary: 30F40
Secondary: 20H10
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References |
Publication
Received: 24 February 2012
Revised: 18 July 2012
Accepted: 4 October 2013
Published: 10 March 2013
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Authors |
| Hyungryul Baik | |
| Department of Mathematics Cornell University 310 Malott Hall Ithaca New York 14853-4201 USA |
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| http://www.math.cornell.edu/~hrbaik/ | |
| Lucien Clavier | |
| Department of Mathematics Cornell University 310 Malott Hall Ithaca New York 14853-4201 USA |
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| http://www.math.cornell.edu/~lpc49/ | |
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