Symplectic and Poisson geometry on b-manifolds

Abstract

Let $M^{2n}$ be a Poisson manifold with Poisson bivector field $\Pi$. We say that $M$ is b-Poisson if the map ${\Pi }^n:M\to {\Lambda }^{2n}(TM)$ 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 $(M,\Pi )$ 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.

34 pages. Some changes have been implemented mainly in Sections 2 and 6. Minor changes in exposition. References have been added

References in corpus (4)

• Lectures on Integrability of Lie Brackets
• Toric actions on b-symplectic manifolds
• Deformations of log-symplectic structures
• Symplectic groupoids of log symplectic manifolds

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