Symplectic and Poisson geometry on b-manifolds

2012/06/30 by Victor Guillemin, Eva Miranda, Ana Rita Pires · 2 citations
Mathematics · #math.SG #math.DG #msc:53D05 #msc:53D17

paper · pdf · doi:10.1016/j.aim.2014.07.032

published as Advances in Mathematics (2014), vol 264, pp. 864-896 · 34 pages. Some changes have been implemented mainly in Sections 2 and 6. Minor changes in exposition. References have been added

arxiv created 2014/02/06 · arxiv updated 2015/07/30

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 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.

Cited by

• Hamiltonian group actions in cosymplectic geometry
• Symplectic algebroids, groupoid Toeplitz operators and deformation quantization

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