Hitchin grafting representations II: Dynamics
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908427841699840 |
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| author | Blayac, Pierre-Louis Hamenstädt, Ursula Marty, Théo Monti, Andrea Egidio |
| author_facet | Blayac, Pierre-Louis Hamenstädt, Ursula Marty, Théo Monti, Andrea Egidio |
| contents | The Hitchin component of the character variety of representations of a surface group $π_1(S)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hitchin grafting representations II: Dynamics Blayac, Pierre-Louis Hamenstädt, Ursula Marty, Théo Monti, Andrea Egidio Differential Geometry Geometric Topology The Hitchin component of the character variety of representations of a surface group $π_1(S)$ 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. |
| title | Hitchin grafting representations II: Dynamics |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2407.07748 |