Poisson smooth structures on stratified symplectic spaces

Details Poisson smooth structures on stratified symplectic spaces Poisson smooth structures on stratified symplectic spaces

2010-11-01

arxiv.org/abs/1011.0462v3

Mathematics

Differential Geometry

revised version, 28 pages

Scientific paper

In this note we introduce the notion of a smooth structure on a stratified space and the notion of a Poisson smooth structure on a stratified symplectic space. We show that these smooth spaces possess several important properties, e.g. the existence of smooth partitions of unity. Furthermore, under a mild condition many properties of a symplectic manifold can be extended to a symplectic stratified space provided with a smooth Poisson structure, e.g. the existence and uniqueness of a Hamiltonian flow, the isomorphism between the Brylinski-Poisson homology and the de Rham homology, the existence of a Hodge structure on a symplectic stratified space. We give many examples of stratified symplectic spaces satisfying these properties.

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