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arXiv · 1507.03894

An introduction to pressure metrics on higher Teichm\"uller spaces

Martin Bridgeman·Richard Canary·Andrés Sambarino
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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.

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Martin Bridgeman, Richard Canary, Andrés Sambarino. 2015-07-14. An introduction to pressure metrics on higher Teichm\"uller spaces. https://arxiv.org/abs/1507.03894

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