A cyclic extension of the earthquake flow I

Abstract

Let $\mathcal{T}$ be Teichmüller space of a closed surface of genus at least $2$. We describe an action of the circle on $\mathcal{T}\times \mathcal{T}$, which limits to the earthquake flow when one of the parameters goes to a measured lamination in the Thurston boundary of $\mathcal{T}$. 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 $\mathcal{T}\times \mathcal{T}$ extends to the product of two copies of the universal Teichmüller space.