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2013 The space of geometric limits of one-generator closed subgroups of $\mathrm{PSL}_2(\mathbb{R})$
Hyungryul Baik, Lucien Clavier
Algebr. Geom. Topol. 13(1): 549-576 (2013). DOI: 10.2140/agt.2013.13.549

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:XY 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 .

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Hyungryul Baik. Lucien Clavier. "The space of geometric limits of one-generator closed subgroups of $\mathrm{PSL}_2(\mathbb{R})$." Algebr. Geom. Topol. 13 (1) 549 - 576, 2013. https://doi.org/10.2140/agt.2013.13.549

Information

Received: 24 February 2012; Revised: 18 July 2012; Accepted: 4 October 2013; Published: 2013
First available in Project Euclid: 19 December 2017

zbMATH: 1266.30031
MathSciNet: MR3116379
Digital Object Identifier: 10.2140/agt.2013.13.549

Subjects:
Primary: 30F40
Secondary: 20H10

Rights: Copyright © 2013 Mathematical Sciences Publishers

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