## Geometry & Topology

### A cyclic extension of the earthquake flow I

#### Abstract

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

#### Article information

Source
Geom. Topol., Volume 17, Number 1 (2013), 157-234.

Dates
Revised: 5 July 2012
Accepted: 13 August 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732522

Digital Object Identifier
doi:10.2140/gt.2013.17.157

Mathematical Reviews number (MathSciNet)
MR3035326

Zentralblatt MATH identifier
1278.57024

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds

#### Citation

Bonsante, Francesco; Mondello, Gabriele; Schlenker, Jean-Marc. A cyclic extension of the earthquake flow I. Geom. Topol. 17 (2013), no. 1, 157--234. doi:10.2140/gt.2013.17.157. https://projecteuclid.org/euclid.gt/1513732522

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