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The space of geometric limits of one-generator closed subgroups of PSL2(ℝ)
Algebraic and Geometric Topology
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 computedoi:10.2140/agt.2013.13.549 fatcat:b2zz4ypllfgzbgspp6nckv4jja