Volume 17, issue 1 (2013)

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A cyclic extension of the earthquake flow I

Francesco Bonsante, Gabriele Mondello and Jean-Marc Schlenker

Geometry & Topology 17 (2013) 157–234
Abstract

Let $\mathsc{T}$ be Teichmüller space of a closed surface of genus at least $2$. We describe an action of the circle on $\mathsc{T}×\mathsc{T}$, which limits to the earthquake flow when one of the parameters goes to a measured lamination in the Thurston boundary of $\mathsc{T}$. This circle action shares some of the main properties of the earthquake flow, for instance it satisfies an extension of Thurston’s Earthquake Theorem and it has a complex extension which is analogous and limits to complex earthquakes. Moreover, a related circle action on $\mathsc{T}×\mathsc{T}$ extends to the product of two copies of the universal Teichmüller space.

Keywords
anti-de Sitter, earthquakes, constant curvature surfaces, space-like surfaces
Primary: 57M50