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An $h$-principle for embeddings transverse to a contact structure
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Given a class of embeddings into a contact or a symplectic manifold, we give a sufficient condition, that we call isocontact or isosymplectic realization, for this class to satisfy a general $h$-principle. The flexibility follows from the $h$-principles for isocontact and isosymplectic embeddings, it provides a framework for classical results, and we give two new applications. Our main result is that embeddings transverse to a contact structure satisfy a full $h$-principle in two cases: if the complement of the embedding is overtwisted, or when the intersection of the image of the formal derivative with the contact structure is strictly contained in a proper symplectic subbundle. We illustrate the general framework on symplectic manifolds by studying the universality of Hamiltonian dynamics on regular level sets via a class of embeddings.
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CARDONA AGUILAR, Robert and PRESAS MATA, Francisco. An $h$-principle for embeddings transverse to a contact structure. Journal Of Topology. 2024. Vol. 17, num. 1. ISSN 1753-8416. [consulted: 9 of August of 2026]. Available at: https://hdl.handle.net/2445/219434