Bending, entropy and proper affine actions of surface groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914344576483328 |
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| author | Bridgeman, Martin Canary, Richard Sambarino, Andres |
| author_facet | Bridgeman, Martin Canary, Richard Sambarino, Andres |
| contents | We show that for any closed surface $S$ there is an explict neighborhood $V$ of the fuchsian locus in quasifuchsian space $\mathsf{QF}(S)$ such that for every representation $ρ\in V$ which is not fuchsian, there is a proper affine action on $\mathfrak{sl}(2,\mathbb{C})$ with linear part $\mathsf{Ad}(ρ)$. We further show that there is a larger neighborhood $U$ of the Fuchsian locus so that every critical point of the entropy function in $U$ lies on the Fuchsian locus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20146 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bending, entropy and proper affine actions of surface groups Bridgeman, Martin Canary, Richard Sambarino, Andres Geometric Topology Dynamical Systems Group Theory We show that for any closed surface $S$ there is an explict neighborhood $V$ of the fuchsian locus in quasifuchsian space $\mathsf{QF}(S)$ such that for every representation $ρ\in V$ which is not fuchsian, there is a proper affine action on $\mathfrak{sl}(2,\mathbb{C})$ with linear part $\mathsf{Ad}(ρ)$. We further show that there is a larger neighborhood $U$ of the Fuchsian locus so that every critical point of the entropy function in $U$ lies on the Fuchsian locus. |
| title | Bending, entropy and proper affine actions of surface groups |
| topic | Geometric Topology Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2602.20146 |