2016/05/15 by François Fillastre, Graham Smith, Fillastre, François +1
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Black Holes and Theoretical Physics #History and Theory of Mathematics
paper · pdf · doi:10.48550/arxiv.1605.04563
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 Teichmüller 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.