Symplectic and Poisson geometry on b-manifolds

Victor Guillemin, Eva Miranda, Ana Rita Pires

Research output: Contribution to journalArticlepeer-review

Abstract

Let M2n be a Poisson manifold with Poisson bivector field Π. We say that M is b-Poisson if the map Πn:M→Λ2n(TM) intersects the zero section transversally on a codimension one submanifold Z⊂ 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 neighborhood of Zand 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.
Original languageEnglish
Pages (from-to)864-896
Number of pages33
JournalAdvances in Mathematics
Volume264
Early online date7 Aug 2014
DOIs
Publication statusE-pub ahead of print - 7 Aug 2014

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