The space of geometric limits of one-generator closed subgroups of PSL2(R)

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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) congruent to PSL2(R), and finding quantities parametrizing the limit cases. Along the way, we investigate under what conditions sequences of maps phi(n): 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.
Publisher
GEOMETRY & TOPOLOGY PUBLICATIONS
Issue Date
2013-03
Language
English
Article Type
Article
Citation

ALGEBRAIC AND GEOMETRIC TOPOLOGY, v.13, no.1, pp.549 - 576

ISSN
1472-2739
DOI
10.2140/agt.2013.13.549
URI
http://hdl.handle.net/10203/221032
Appears in Collection
MA-Journal Papers(저널논문)
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