An introduction to pressure metrics on higher Teichm\"uller spaces
Differential Geometry
2017-08-15 v3
Abstract
We discuss how one uses the thermodynamic formalism to produce metrics on higher Teichm\"uller spaces. Our higher Teichm\"uller 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 Teichm\"uller 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 "\emph{The pressure metric for Anosov representations}" and discusses questions and open problems which arise.
Keywords
Cite
@article{arxiv.1507.03894,
title = {An introduction to pressure metrics on higher Teichm\"uller spaces},
author = {Martin Bridgeman and Richard Canary and Andrés Sambarino},
journal= {arXiv preprint arXiv:1507.03894},
year = {2017}
}