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arXiv · 1206.2020

Symplectic and Poisson geometry on b-manifolds

Victor Guillemin·Eva Miranda·Ana Rita Pires
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Abstract

Let $M^{2n}$ be a Poisson manifold with Poisson bivector field $Π$. We say that $M$ is b-Poisson if the map $Π^n:M\toΛ^{2n}(TM)$ intersects the zero section transversally on a codimension one submanifold $Z\subset M$. This paper will be a systematic investigation of such Poisson manifolds. In particular, we will study in detail the structure of $(M,Π)$ in the neighbourhood of $Z$ and using symplectic techniques define topological invariants which determine the structure up to isomorphism. We also investigate a variant of de Rham theory for these manifolds and its connection with Poisson cohomology.

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Victor Guillemin, Eva Miranda, Ana Rita Pires. 2014-02-06. Symplectic and Poisson geometry on b-manifolds. https://doi.org/10.1016/j.aim.2014.07.032

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