Relative h-principle and contact geometry

Taylor, Jacob

doi:10.2140/agt.2025.25.267

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ISSN (electronic): 1472-2739

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Relative $h$-principle and contact geometry

Jacob Taylor

Algebraic & Geometric Topology 25 (2025) 267–285

DOI: 10.2140/agt.2025.25.267

Abstract

We show that if $F (M)$ is a space of holonomic solutions with space of formal solutions $F^{f} (M)$ that satisfies a certain relative $h$ -principle, then the nonrelative 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 and Murphy to find infinite cyclic subgroups in the homotopy groups of contactomorphism groups.

Keywords

contact geometry, $h$-principle

Mathematical Subject Classification

Primary: 53D35, 57R17

Secondary: 58D99

References

Publication

Received: 29 March 2023

Revised: 18 December 2023

Accepted: 31 January 2024

Published: 5 March 2025

Authors

Jacob Taylor
Department of Mathematics University of Toronto Toronto, ON Canada

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Volume 25, issue 1 (2025)