Relative H-Principle and Contact Geometry

Jacob Taylor

doi:10.2140/agt.2025.25.267

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arXiv · 2210.03185

Relative H-Principle and Contact Geometry

Jacob Taylor

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Abstract

We show that if $F(M)$ is some space of holonomic solutions with space of formal solutions $F^f(M)$ that satisfies a certain relative $h$-principle, then the non-relative map $F(M) \to F^f(M)$ admits a section up to homotopy. We apply this to the relative $h$-principle for overtwisted contact structures proved by Borman-Eliashberg-Murphy to find infinite cyclic subgroups in the homotopy groups of the contactomorphism group of $M$.

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Jacob Taylor. 2022-10-06. Relative H-Principle and Contact Geometry. https://doi.org/10.2140/agt.2025.25.267

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