Jiggling: an h-principle without homotopical assumptions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911102619615232 |
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| author | Fokma, Anna del Pino, Álvaro Toussaint, Lauran |
| author_facet | Fokma, Anna del Pino, Álvaro Toussaint, Lauran |
| contents | The jiggling lemma of Thurston shows that any triangulation can be jiggled (read: subdivided and then perturbed) to be in general position with respect to a distribution. Our main result is a generalization of Thurston's lemma. It states that piecewise smooth solutions of a given open and fiberwise dense differential relation $\mathcal{R} \subset J^1(E)$ of first order can be constructed by jiggling arbitrary sections of $E$. Our statement also holds in parametric and relative form. We understand this as an h-principle without homotopical assumptions for piecewise smooth solutions of $\mathcal{R}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_13627 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jiggling: an h-principle without homotopical assumptions Fokma, Anna del Pino, Álvaro Toussaint, Lauran Geometric Topology Differential Geometry 57R45 (Primary) 57Q65, 57R05, 57R35 (Secondary) The jiggling lemma of Thurston shows that any triangulation can be jiggled (read: subdivided and then perturbed) to be in general position with respect to a distribution. Our main result is a generalization of Thurston's lemma. It states that piecewise smooth solutions of a given open and fiberwise dense differential relation $\mathcal{R} \subset J^1(E)$ of first order can be constructed by jiggling arbitrary sections of $E$. Our statement also holds in parametric and relative form. We understand this as an h-principle without homotopical assumptions for piecewise smooth solutions of $\mathcal{R}$. |
| title | Jiggling: an h-principle without homotopical assumptions |
| topic | Geometric Topology Differential Geometry 57R45 (Primary) 57Q65, 57R05, 57R35 (Secondary) |
| url | https://arxiv.org/abs/2501.13627 |