The Space of Geometric Limits of One-generator Closed Subgroups of PSL2(R) release_cy6tsxbl3nci5ix3pphkjcm52q

by Hyungryul Baik, Lucien Clavier

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2012  

Abstract

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 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 PSL2(R) only by looking at the Hausdorff limit of some closed subsets of C.
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Date   2012-02-07
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arXiv  1202.1365v1
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