Anti-de Sitter geometry and Teichm\"uller theory
Abstract
The aim of these notes is to provide an introduction to Anti-de Sitter geometry, with special emphasis on dimension three and on the relations with Teichm\"uller theory, whose study has been initiated by the seminal paper of Geoffrey Mess in 1990. In the first part we give a broad introduction to Anti-de Sitter geometry in any dimension. The main results of Mess, including the classification of maximal globally hyperbolic Cauchy compact manifolds and the construction of the Gauss map, are treated in the second part. Finally, the third part contains related results which have been developed after the work of Mess, with the aim of giving an overview on the state-of-the-art.
Keywords
Cite
@article{arxiv.2004.14414,
title = {Anti-de Sitter geometry and Teichm\"uller theory},
author = {Francesco Bonsante and Andrea Seppi},
journal= {arXiv preprint arXiv:2004.14414},
year = {2021}
}
Comments
79 pages, 14 figures. The final version of this paper will appear in the book: In the tradition of Thurston (ed. V. Alberge, K. Ohshika and A. Papadopoulos), Springer Verlag, 2020