Generically nondegenerate Poisson structures and their Lie algebroids

Poisson geometry;symplectic geometry

Lanius, Melinda Dawn

关键词: Poisson geometry;    symplectic geometry;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/101536/LANIUS-DISSERTATION-2018.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

In this dissertation, generically nondegenerate Poisson manifolds are studied by lifting them to a Lie algebroid where they can be understood as nondegenerate. This allows standard tools of symplectic geometry to be applied to concretely describe the behavior of the Poisson structure. This study encompasses various Poisson structures and Lie algebroids previously studied in the literature while also developing several new types. The powerful language of Lie algebroids is applied to the computation of Poisson cohomology in a novel way and to the classification of new classes of compact oriented Poisson surfaces.