Symplectic and Poisson geometry on b-manifolds
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Guillemin_Symplectic and.pdf
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Author(s)
Guillemin, Victor W
Miranda, Eva
Pissarra Pires, Ana Rita
Date Issued
April 21, 2017
Journal
Advances in Mathematics
Publisher
Elsevier
Citation
Guillemin, Victor; Miranda, Eva and Pires, Ana Rita. “Symplectic and Poisson Geometry on b-Manifolds.” Advances in Mathematics 264 (October 2014): 864–896. © 2014 Elsevier Inc
Version
Original manuscript
Abstract
Let M2nM2n be a Poisson manifold with Poisson bivector field Π. We say that M is b -Poisson if the map Πn:M→Λ2n(TM)Πn:M→Λ2n(TM) intersects the zero section transversally on a codimension one submanifold Z⊂MZ⊂M. This paper will be a systematic investigation of such Poisson manifolds. In particular, we will study in detail the structure of (M,Π)(M,Π) in the neighborhood 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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.aim.2014.07.032
