Geodesic
The space of geometric limits of one-generator closed subgroups of PSL2(ℝ)
Baik, Hyungryul1 ; Clavier, Lucien1
1Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, New York 14853-4201, USA
Algebraic and Geometric Topology, Tome 13 (2013) no. 1, pp. 549-576
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We give a complete description of the closure of the space of one-generator closed subgroups of PSL2(ℝ) for the Chabauty topology, by computing explicitly the matrices associated with elements of Aut(D)≅PSL2(ℝ), 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(ℝ) only by looking at the Hausdorff limit of some closed subsets of ℂ.

DOI : 10.2140/agt.2013.13.549
Classification : 30F40, 20H10
Keywords: PSL2(R), Chabauty topology, Hausdorff topology, geometric limit

Baik, Hyungryul  1   ; Clavier, Lucien  1

1 Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, New York 14853-4201, USA 
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Baik, Hyungryul; Clavier, Lucien. The space of geometric limits of one-generator closed subgroups of PSL2(ℝ). Algebraic and Geometric Topology, Tome 13 (2013) no. 1, pp. 549-576. doi: 10.2140/agt.2013.13.549

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