Jiggling: an h-principle without homotopical assumptions

Anna Fokma; Álvaro del Pino; Lauran Toussaint

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arXiv · 2501.13627

Jiggling: an h-principle without homotopical assumptions

Anna Fokma·Álvaro del Pino·Lauran Toussaint

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Abstract

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 $\mathcal{R}$.

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Anna Fokma, Álvaro del Pino, Lauran Toussaint. 2025-01-23. Jiggling: an h-principle without homotopical assumptions. https://arxiv.org/abs/2501.13627

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