Pressure metrics for cusped Hitchin components

Harrison Bray; Richard Canary; Lien-Yung Kao; Giuseppe Martone

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arXiv · 2111.07493

Pressure metrics for cusped Hitchin components

Harrison Bray·Richard Canary·Lien-Yung Kao·Giuseppe Martone

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Abstract

We study the cusped Hitchin component consisting of (conjugacy classes of) cusped Hitchin representations of a torsion-free geometrically finite Fuchsian group into PSL(d,R). We produce pressure metrics associated to the first fundamental weight and the first simple root. When $d=3$ we produce a pressure metric associated to the Hilbert length, which is new even when the Fuchsian group is cocompact.

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Harrison Bray, Richard Canary, Lien-Yung Kao, Giuseppe Martone. 2021-11-15. Pressure metrics for cusped Hitchin components. https://arxiv.org/abs/2111.07493

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