On the existence of symplectic realizations
Marius Crainic, Ioan Marcut
TL;DR
This paper provides a direct global proof demonstrating that any Poisson manifold admits a symplectic realization, establishing a fundamental link between Poisson and symplectic geometry.
Contribution
It offers a new, direct global proof for the existence of symplectic realizations of arbitrary Poisson manifolds, simplifying previous approaches.
Findings
Confirmed the existence of symplectic realizations for all Poisson manifolds.
Provided a constructive global proof method.
Enhanced understanding of the relationship between Poisson and symplectic structures.
Abstract
We give a direct global proof for the existence of symplectic realizations of arbitrary Poisson manifolds.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry