The Anti-de Sitter proof of Thurston's earthquake theorem

Farid Diaf; Andrea Seppi

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arXiv · 2306.03631

The Anti-de Sitter proof of Thurston's earthquake theorem

Farid Diaf·Andrea Seppi

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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 $\mathrm{PSL}(2,\mathbb R)$, 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.

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Farid Diaf, Andrea Seppi. 2023-06-06. The Anti-de Sitter proof of Thurston's earthquake theorem. https://arxiv.org/abs/2306.03631

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