Erschienen:
Cambridge University Press (CUP), 2018
Erschienen in:
Ergodic Theory and Dynamical Systems, 38 (2018) 6, Seite 2001-2035
Sprache:
Englisch
DOI:
10.1017/etds.2016.111
ISSN:
0143-3857;
1469-4417
Entstehung:
Anmerkungen:
Beschreibung:
<jats:p>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 and Sambarino, <jats:italic>The pressure metric for Anosov representations</jats:italic>, and discusses questions and open problems which arise.</jats:p>