Relative h-principle and contact geometry

Taylor, Jacob¹

¹Department of Mathematics, University of Toronto, Toronto, ON, Canada

Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 267-285

Résumé

We show that if F(M) is a space of holonomic solutions with space of formal solutions Ff(M) that satisfies a certain relative h-principle, then the nonrelative map F(M) → Ff(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.

Détail

DOI : 10.2140/agt.2025.25.267

Keywords: contact geometry, $h$-principle

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