University of Illinois Urbana-Champaign

Generically nondegenerate Poisson structures and their Lie algebroids

Lanius, Melinda Dawn

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

Description

Title
Generically nondegenerate Poisson structures and their Lie algebroids
Author(s)
Lanius, Melinda Dawn
Issue Date
2018-07-06
Director of Research (if dissertation) or Advisor (if thesis)
Albin, Pierre
Doctoral Committee Chair(s)
Tolman, Susan
Committee Member(s)
  • Lerman, Eugene
  • Loja Fernandes, Rui
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
Graduation Semester
2018-08
Type of Resource
text
Permalink
http://hdl.handle.net/2142/101536
Copyright and License Information
Copyright 2018 by Melinda Lanius. All rights reserved.

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