The Anti-de Sitter Proof of Thurston’s Earthquake Theorem

Farid Diaf () and Andrea Seppi ()
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Farid Diaf: University of Grenoble Alpes
Andrea Seppi: University of Grenoble Alpes

Chapter Chapter 4 in In the Tradition of Thurston III, 2024, pp 67-104 from Springer

Abstract: Abstract Thurston’s earthquake theorem asserts that every orientation-preserving homeomorphism of the circle admits an extension to the hyperbolic plane which is a (left or right) earthquake. The purpose of these notes is to provide a proof of Thurston’s earthquake theorem, using the bi-invariant geometry of the Lie group PSL ( 2 , ℝ ) $$\mathrm {PSL}(2,\mathbb R)$$ , which is also called Anti-de Sitter three-space. The involved techniques are elementary, and no background knowledge is assumed apart from some two-dimensional hyperbolic geometry.

Keywords: Hyperbolic geometry; Teichmüller theory; Anti-de Sitter geometry; 30F60; 53C50; 57M50 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/978-3-031-43502-7_4

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