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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
- Date of Ingest
- 2018-09-27T16:17:40Z
- 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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