2015/07/14 by Bridgeman, Martin, Canary, Richard, Sambarino, Andrés
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1507.03894
We discuss how one uses the thermodynamic formalism to produce metrics on higher Teichmüller spaces. Our higher Teichmüller spaces will be spaces of Anosov representations of a word-hyperbolic group into a semi-simple Lie group. We begin by discussing our construction in the classical setting of the Teichmüller space of a closed orientable surface of genus at least 2, then we explain the construction for Hitchin components and finally we treat the general case. This paper surveys results of Bridgeman-Canary-Labourie-Sambarino "The pressure metric for Anosov representations" and discusses questions and open problems which arise.