Wild globally hyperbolic maximal anti-de Sitter structures

Abstract

Let $\Sigma$ be a connected, oriented surface with punctures and negative Euler characteristic. We introduce wild globally hyperbolic anti-de Sitter structures on $\Sigma \times \mathbb{R}$ and provide two parameterisations of their deformation space: as a quotient of the product of two copies of the Teichmüller space of crowned hyperbolic surfaces and as the bundle over the Teichmüller space of $\Sigma$ of meromorphic quadratic differentials with poles of order at least $3$ at the punctures.

27 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1806.08176