Generically nondegenerate Poisson structures and their Lie algebroids

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Lanius, Melinda Dawn

Contributors dc:contributor

• Albin, Pierre
• Tolman, Susan
• Lerman, Eugene
• Loja Fernandes, Rui

• Poisson geometry
• symplectic geometry

Statement dc:rights

• Copyright 2018 by Melinda Lanius. All rights reserved.

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101536

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101536