Haefliger structures and symplectic/contact structures

François Laudenbach, Gaël Meigniez
2016 Journal de l'École polytechnique. Mathématiques  
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
more » ... 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. 2010 Mathematics Subject Classification. 57R17, 57R30.
doi:10.5802/jep.27 fatcat:qlvu6uds6navlisk36fzmsr32y