scholarly journals Poisson cohomology of regular Poisson manifolds

1992 ◽  
Vol 42 (4) ◽  
pp. 967-988 ◽  
Author(s):  
Ping Xu
Keyword(s):  
Poisson Manifolds ◽  
Poisson Cohomology

scholarly journals Poisson manifolds of compact types (PMCT 1)

2019 ◽  
Vol 2019 (756) ◽  
pp. 101-149 ◽  
Author(s):  
Marius Crainic ◽  
Rui Loja Fernandes ◽  
David Martínez Torres
Keyword(s):  
Compact Manifold ◽  
Hodge Decomposition ◽  
Affine Geometry ◽  
Poisson Manifolds ◽  
Circle Action ◽  
Lie Theory ◽  
De Rham Cohomology ◽  
Fundamental Properties ◽  
Poisson Cohomology ◽  
De Rham

AbstractThis is the first in a series of papers dedicated to the study of Poisson manifolds of compact types (PMCTs). This notion encompasses several classes of Poisson manifolds defined via properties of their symplectic integrations. In this first paper we establish some fundamental properties and constructions of PMCTs. For instance, we show that their Poisson cohomology behaves very much like the de Rham cohomology of a compact manifold (Hodge decomposition, non-degenerate Poincaré duality pairing, etc.) and that the Moser trick can be adapted to PMCTs. More important, we find unexpected connections between PMCTs and symplectic topology: PMCTs are related with the theory of Lagrangian fibrations and we exhibit a construction of a non-trivial PMCT related to a classical question on the topology of the orbits of a free symplectic circle action. In subsequent papers, we will establish deep connections between PMCTs and integral affine geometry, Hamiltonian G-spaces, foliation theory, orbifolds, Lie theory and symplectic gerbes.

Prequantizable Poisson manifolds and Jacobi structures

1996 ◽  
Vol 29 (19) ◽  
pp. 6313-6324 ◽  
Author(s):  
Domingo Chinea ◽  
Juan C Marrero ◽  
Manuel de León
Keyword(s):  
Poisson Manifolds

scholarly journals Classical and variational Poisson cohomology

2021 ◽  
Author(s):  
Bojko Bakalov ◽  
Alberto De Sole ◽  
Reimundo Heluani ◽  
Victor G. Kac ◽  
Veronica Vignoli
Keyword(s):  
Poisson Cohomology
Sign in / Sign up

Export Citation Format

Share Document