A h-principle for symplectic foliations

Details A h-principle for symplectic foliations A h-principle for symplectic foliations

2010-10-17

arxiv.org/abs/1010.3447v2

Mathematics

Symplectic Geometry

9 pages; final version accepted for publication by IMRN

Scientific paper

We show that a classical result of Gromov in symplectic geometry extends to the context of symplectic foliations, which we regard as a $h$-principle for (regular) Poisson geometry. Namely, we formulate a sufficient cohomological criterion for a regular bivector to be homotopic to a regular Poisson structure, in the spirit of Haefliger's criterion for homotoping a distribution to a foliation. We give an example to show that this criterion is not too unsharp.

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