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Albin, Pierre Tolman, Susan Lerman, Eugene Loja Fernandes, Rui Lanius, Melinda Dawn 2018-09-27T16:17:40Z 2018-09-27T16:17:40Z 2018-07-06 2018-08 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms The student, Melinda Lanius, accepted the attached license on 2018-07-05 at 18:31. The student, Melinda Lanius, submitted this Dissertation for approval on 2018-07-05 at 18:33. This Dissertation was approved for publication on 2018-07-06 at 13:14. DSpace SAF Submission Ingestion Package generated from Vireo submission #12746 on 2018-09-27 at 10:46:56 Made available in DSpace on 2018-09-27T16:17:40Z (GMT). No. of bitstreams: 2 LANIUS-DISSERTATION-2018.pdf: 1937827 bytes, checksum: 5d7f6de3bb69a2cc375e9177fbe8fbc4 (MD5) LICENSE.txt: 4211 bytes, checksum: b53f36ad88689347dbcd7cf741ad0e33 (MD5) Previous issue date: 2018-07-06 application/pdf http://hdl.handle.net/2142/101536 en Copyright 2018 by Melinda Lanius. All rights reserved. Poisson geometry symplectic geometry Generically nondegenerate Poisson structures and their Lie algebroids text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.