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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

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.

anti-de Sitter, earthquakes, constant curvature surfaces, space-like surfaces
Mathematical Subject Classification 2010
Primary: 57M50
Received: 6 September 2011
Revised: 5 July 2012
Accepted: 13 August 2012
Published: 26 February 2013
Proposed: Benson Farb
Seconded: Walter Neumann, David Gabai
Francesco Bonsante
Dipartimento do Matematica
Università degli Studi di Pavia
Via Ferrata
I-27100 Pavia
Gabriele Mondello
Università di Roma “La Sapienza”
Dipartimento di Matematica “Guido Castelnuovo”
Piazzale Aldo Moro 5
I-00185 Roma
Jean-Marc Schlenker
Institut de Mathématiques de Toulouse
Université Paul Sabatier
118 route de Narbonne
F-31062 Toulouse Cedex 9