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arXiv · 2407.07748

Hitchin grafting representations II: Dynamics

Pierre-Louis Blayac·Ursula Hamenstädt·Théo Marty·Andrea Egidio Monti
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Abstract

The Hitchin component of the character variety of representations of a surface group $\pi_1(S)$ into $\mathrm{PSL}_d(\mathbb{R})$ for some $d \geq 3$ can be equipped with a pressure metric whose restriction to the Fuchsian locus equals the Weil--Petersson metric up to a constant factor. We show that if the genus of $S$ is at least $3$, then the Fuchsian locus contains quasi-convex subsets of infinite diameter for the Weil--Petersson metric whose diameter for the path metric of the pressure metric is finite. This is established through showing that biinfinite paths of bending deformations have controlled bounded length.

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Pierre-Louis Blayac, Ursula Hamenstädt, Théo Marty, Andrea Egidio Monti. 2024-07-10. Hitchin grafting representations II: Dynamics. https://arxiv.org/abs/2407.07748

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