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A Poisson structure on a smooth manifold $M$ is a map $C^\infty(M)\times C^\infty(M)\times C^\infty(M)$ satisfying certain conditions. For a vector space $V$, we can talk about a Poisson structure on …

It turns out that linear Poisson structure need not (or should not) give a Poisson structure on the fibers. But, the conclusion that a linear Poisson structure on a vector bundle $E\rightarrow M$ shou …

I am reading the paper Grothendieck groups of Poisson vector bundles by Viktor L. Ginzburg. In that paper, the author introduces a new invariant for Poisson manifolds; which is called as the Poisson …

I am trying to see if there is any existing cohomology theory for Dirac manifolds. For the case of poisson manifolds, we have the notion of Poisson cohomology. For a manifold $M$, one can consider the …

Even though we may not be able to associate a Lie algebroid with a singular foliation, we can associate a Lie $\infty$-algebroid with a singular foliation (satisfying certain not so strange conditions …