A cyclic extension of the earthquake flow I

Bonsante, Francesco¹ ; Mondello, Gabriele² ; Schlenker, Jean-Marc³

¹ Dipartimento do Matematica, Università degli Studi di Pavia, Via Ferrata, 1, I-27100 Pavia, Italy
² Università di Roma “La Sapienza”, Dipartimento di Matematica “Guido Castelnuovo”, Piazzale Aldo Moro 5, I-00185 Roma, Italy
³ Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France

Geometry & topology, Tome 17 (2013) no. 1, pp. 157-234.

Résumé

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.

Détail

DOI : 10.2140/gt.2013.17.157

Classification : 57M50
Keywords: anti-de Sitter, earthquakes, constant curvature surfaces, space-like surfaces

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