A Fréchet topology on measured laminations and Earthquakes in the hyperbolic plane

Details A Fréchet topology on measured laminations and Earthquakes in the hyperbolic plane A Fréchet topology on measured laminations and Earthquakes in the hyperbolic plane

2010-06-04

arxiv.org/abs/1006.0941v1

Mathematics

Geometric Topology

31 pages, 7 figures

Scientific paper

We prove that the bijective correspondence between the space of bounded measured laminations $ML_b(\mathbb{H})$ and the universal Teichm\"uller space $T(\mathbb{H})$ given by $\lambda\mapsto E^{\lambda}|_{S^1}$ is a homeomorphism for the Fr\'echet topology on $ML_b(\mathbb{H})$ and the Teichm\"uller topology on $T(\mathbb{H})$, where $E^{\lambda}$ is an earthquake with earthquake measure $\lambda$. A corollary is that earthquakes with discrete earthquake measures are dense in $T(\mathbb{H})$. We also establish infinitesimal versions of the above results.

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