A foliation is a partition of a manifold into connected immersed submanifolds. However this definition does not provide information on the "dynamics", i.e. on the vector fields that induce the foliation. We define a singular foliation as a submodule of the module of vector fields that is involutive and finitely generated. We show that if this singular foliation admits a resolution by a complex of vector bundles, then we can lift the bracket of the vector fields to a Lie infinity-algebroid structure on the resolution. This construction is universal in the sense that any two choices of resolutions and lifting give isomorphic Lie infinity-algebroid structures (up to homotopy). This construction may be a first step toward the construction of cohomology for singular foliations, and /or characteristic/modular classes etc. Due to the amount of material, part II of this talk is scheduled for May 24.
Wednesday, May 10, 2017 - 2:00pm