A Fréchet topology on measured laminations and Earthquakes in the hyperbolic plane - Mathematics > Geometric Topology

A Fréchet topology on measured laminations and Earthquakes in the hyperbolic plane - Mathematics > Geometric Topology - Download this document for free, or read online. Document in PDF available to download.

Abstract: We prove that the bijective correspondence between the space of boundedmeasured laminations $ML b\mathbb{H}$ and the universal Teichm\-uller space$T\mathbb{H}$ given by $\lambda\mapsto E^{\lambda}| {S^1}$ is a homeomorphismfor the Fr\-echet topology on $ML b\mathbb{H}$ and the Teichm\-uller topologyon $T\mathbb{H}$, where $E^{\lambda}$ is an earthquake with earthquakemeasure $\lambda$. A corollary is that earthquakes with discrete earthquakemeasures are dense in $T\mathbb{H}$. We also establish infinitesimal versionsof the above results.

Author: Hideki Miyachi, Dragomir Saric

Source: https://arxiv.org/