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Anti-de Sitter Geometry and Teichmüller Theory

In: In the Tradition of Thurston

Author

Listed:
  • Francesco Bonsante

    (Università degli Studi di Pavia, Dipartimento di Matematica “Felice Casorati”)

  • Andrea Seppi

    (CNRS and Université Grenoble Alpes)

Abstract

The aim of this chapter is to provide an introduction to Anti-de Sitter geometry, with special emphasis on dimension three and on the relations with Teichmüller 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.

Suggested Citation

  • Francesco Bonsante & Andrea Seppi, 2020. "Anti-de Sitter Geometry and Teichmüller Theory," Springer Books, in: Ken’ichi Ohshika & Athanase Papadopoulos (ed.), In the Tradition of Thurston, chapter 0, pages 545-643, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-55928-1_15
    DOI: 10.1007/978-3-030-55928-1_15
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