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Chapitre D'ouvrage Année : 2018

Group actions and scattering problems in Teichmüller theory

Résumé

In recent years, Teichmüller theory, which is the study of moduli spaces of marked Riemann surfaces, has come to be considered more and more from the point of view of actions of surface groups inside certain semi-simple Lie groups. In particular, we consider the case where the Lie groups in question have symmetric spaces which are lorentzian spacetimes. Indeed, this can be considered as the starting point of Mess' seminal work, which led to the development of new and strikingly simpler proofs of many results of Teichm\"uller theory by considering them in terms of geometric objects inside these symmetric spaces. Our aim is to provide a brief and straightforward introduction to this approach, whilst developing what we consider to be a useful mental framework for organising known results and open problems.
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Dates et versions

hal-01316186 , version 1 (15-05-2016)

Identifiants

  • HAL Id : hal-01316186 , version 1

Citer

François Fillastre, Graham Smith. Group actions and scattering problems in Teichmüller theory. Handbook of Group Actions III, 40, International Press of Boston; Higher Education Press, pp.359--420, 2018, Advanced Lectures in Mathematics, 157146364X. ⟨hal-01316186⟩
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