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Article Dans Une Revue Journal de l'École polytechnique — Mathématiques Année : 2016

Haefliger structures and symplectic/contact structures

Résumé

For some geometries including symplectic and contact structures on an n-dimensional manifold, we introduce a two-step approach to Gromov's h-principle. From formal geometric data, the first step builds a transversely geometric Haefliger structure of codimension n. This step works on all manifolds, even closed. The second step, which works only on open manifolds and for all geometries, regularizes the intermediate Haefliger structure and produces a genuine geometric structure. Both steps admit relative parametric versions. The proofs borrow ideas from W. Thurston, like jiggling and inflation. Actually, we are using a more primitive jiggling due to R. Thom.
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Dates et versions

hal-01119725 , version 1 (23-02-2015)
hal-01119725 , version 2 (06-07-2015)
hal-01119725 , version 3 (25-01-2016)

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Francois Laudenbach, Gael Gael Meigniez. Haefliger structures and symplectic/contact structures. Journal de l'École polytechnique — Mathématiques, 2016, 3, pp.1-19. ⟨hal-01119725v3⟩
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