  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.

Geometric Topology;Differential Geometry