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The Space of Geometric Limits of One-generator Closed Subgroups of
PSL2(R)
release_cy6tsxbl3nci5ix3pphkjcm52q
by
Hyungryul Baik, Lucien Clavier
Released
as a article
.
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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1202.1365v1
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