#### 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
##### Publication
Received: 6 September 2011
Revised: 5 July 2012
Accepted: 13 August 2012
Published: 26 February 2013
Proposed: Benson Farb
Seconded: Walter Neumann, David Gabai
##### Authors
 Francesco Bonsante Dipartimento do Matematica Università degli Studi di Pavia Via Ferrata 1 I-27100 Pavia Italy http://www-dimat.unipv.it/~bonsante/ Gabriele Mondello Università di Roma “La Sapienza” Dipartimento di Matematica “Guido Castelnuovo” Piazzale Aldo Moro 5 I-00185 Roma Italy http://www.mat.uniroma1.it/people/mondello/ Jean-Marc Schlenker Institut de Mathématiques de Toulouse Université Paul Sabatier 118 route de Narbonne F-31062 Toulouse Cedex 9 France http://www.math.univ-toulouse.fr/~schlenker/