Cohomology in algebra, geometry, physicsand statistics

Morita equivalence of singular Riemannian foliations and I-Poisson geometry

We recall the notion of singular foliations and show how to extend it in a compatible way to the presence of a Riemannian metric. Morita equivalence of such structures provides an equivalence relation on the geometry transverse to the leaves. Finally we extend  ``coisotropic submanifolds of a Poisson manifold” to potentially singular subspaces, yielding what we call an I-Poisson structure, and use this notion to construct an invariant of singular Riemannian foliations under the above-mentioned Morita equivalence. 
This is joint work in progress with Hadi Nahari.
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