Flexibility and degeneracy around a theorem of Thurston
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917124756209664 |
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| author | Nolte, Alexander |
| author_facet | Nolte, Alexander |
| contents | We give two flexible and degenerate constructions related to a theorem of Thurston. First, we produce geodesic segments for Thurston's asymmetric metric on Teichmüller space $\mathcal{T}(S_g)$ that remain geodesics after adding arbitrary $\varepsilon$-Lipschitz noise to all but one Fenchel-Nielsen coordinate. Then, for all $2 < n \leq 3g-3$ we construct open sets in $\mathcal{T}(S_g)^n$ for which the limit cones of the corresponding representations in $\mathrm{PSL}_2(\mathbb{R})^n$ are cones over explicit finite-sided polyhedra. Each construction is as degenerate as possible and has applications to the basic structure and local non-rigidity of the involved objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04685 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Flexibility and degeneracy around a theorem of Thurston Nolte, Alexander Geometric Topology Differential Geometry 57K20, 20H10, 22E40 We give two flexible and degenerate constructions related to a theorem of Thurston. First, we produce geodesic segments for Thurston's asymmetric metric on Teichmüller space $\mathcal{T}(S_g)$ that remain geodesics after adding arbitrary $\varepsilon$-Lipschitz noise to all but one Fenchel-Nielsen coordinate. Then, for all $2 < n \leq 3g-3$ we construct open sets in $\mathcal{T}(S_g)^n$ for which the limit cones of the corresponding representations in $\mathrm{PSL}_2(\mathbb{R})^n$ are cones over explicit finite-sided polyhedra. Each construction is as degenerate as possible and has applications to the basic structure and local non-rigidity of the involved objects. |
| title | Flexibility and degeneracy around a theorem of Thurston |
| topic | Geometric Topology Differential Geometry 57K20, 20H10, 22E40 |
| url | https://arxiv.org/abs/2512.04685 |