标题： Thurston 地震定理的反德西特证明 显示英文标题

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

摘要： Thurston的地震定理指出，圆的每个保持方向的同胚都可以扩展为双曲平面的一个（左或右）地震。 这些笔记的目的是使用李群$\mathrm{PSL}(2,\mathbb R)$的双不变几何来证明Thurston的地震定理，该李群也称为反德西特三维空间。 所涉及的技术是基本的，除了某些二维双曲几何知识外，不假设其他背景知识。 显示英文摘要

摘要： 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.