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Title:Generically nondegenerate Poisson structures and their Lie algebroids
Author(s):Lanius, Melinda Dawn
Director of Research:Albin, Pierre
Doctoral Committee Chair(s):Tolman, Susan
Doctoral Committee Member(s):Lerman, Eugene; Loja Fernandes, Rui
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Poisson geometry
symplectic geometry
Abstract: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.
Issue Date:2018-07-06
Rights Information:Copyright 2018 by Melinda Lanius. All rights reserved.
Date Available in IDEALS:2018-09-27
Date Deposited:2018-08

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