Symplectic and Poisson geometry on b-manifolds
By V. Guillemin, Eva Miranda, A. R. Pires. 2012
180 citations recorded by the source corpus.
Abstract Let M 2 n be a Poisson manifold with Poisson bivector field Π. We say that M is b-Poisson if the map Π n : M → Λ 2 n ( T M ) 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 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.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/33efa96801756992398b34da0aed06aa02ddb602
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In Mathematical Physics
Citations in the corpus
- Toric Actions on b-Symplectic Manifolds (2013, methodology): “Another ingredient is Radko’s classification of b-symplectic structures on a compact surface M , up to b-symplectomorphism, by the set of curves Z, their modular periods and the regularized Liouville volume (see Theorem 3 in [R] or Theorem 17 in [GMP2]).”