A cyclic extension of the earthquake flow

Details A cyclic extension of the earthquake flow A cyclic extension of the earthquake flow

2011-06-02

arxiv.org/abs/1106.0525v1

Mathematics

Geometric Topology

39 pages, 5 figures

Scientific paper

Let $\cT$ be Teichm\"uller space of a closed surface of genus at least 2. For any point $c\in \cT$, we describe an action of the circle on $\cT\times \cT$, which limits to the earthquake flow when one of the parameters goes to a measured lamination in the Thurston boundary of $\cT$. 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 $\cT\times \cT$ extends to the product of two copies of the universal Teichm\"uller space.

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