2026-09-22T13:04:40Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/124365 2024-09-16 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Loja Fernandes, Rui A Lerman, Eugene M Junge, Marius Berwick Evans, Daniel 2024-05 application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms The student, Luka Zwaan, accepted the attached license on 2024-04-22 at 15:20. The student, Luka Zwaan, submitted this Dissertation for approval on 2024-04-22 at 15:30. This Dissertation was approved for publication on 2024-04-23 at 16:24. DSpace SAF Submission Ingestion Package generated from Vireo submission #20545 on 2024-09-16 at 00:35:47 Duistermaat-Heckman measures for Hamiltonian groupoid actions Zwaan, Luka Marinus Simon 2024-04-23 Poisson Manifolds Hamiltonian Actions Symplectic Groupoids Integral Affine Structures This thesis treats two problems related to Poisson manifolds of compact types: the existence of Poisson manifolds of strong compact type, and the generalisation of classical Duistermaat-Heckman results to the setting of Hamiltonian actions of symplectic groupoids. In Chapter 4 we prove that all strongly affine circles and 2-tori appear as the leaf space of a regular Poisson manifold of strong compact type. These Poisson manifolds are all fibrations over their leaf space with symplectic leaves diffeomorphic to the smooth manifold underlying a K3 surface. In Chapter 5 we show that for a Hamiltonian action of a regular, source proper symplectic groupoid with sufficiently nice properties there is an analogue of the Duistermaat-Heckman measure which is a polynomial measure with respect to the natural integral affine structure. Text eng https://hdl.handle.net/2142/124365 Copyright 2024 Luka Marinus Simon Zwaan Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics