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Title:Stacks in Poisson geometry
Author(s):Villatoro, Joel David
Director of Research:Fernandes, Rui
Doctoral Committee Chair(s):Lerman, Eugene
Doctoral Committee Member(s):Albin, Pierre; Pascaleff, James
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Stacks, Differential Manifolds, Poisson Manifolds, Symplectic Manifolds.
Abstract:This thesis is divided into four chapters. The first chapter discusses the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between the bicategory of internal groupoids and the bicategory of geometric stacks. The second chapter discusses standard concepts in the theory of geometric stacks, including Morita equivalence, stack symmetries, and some Morita invariants. The third chapter introduces a new site of Dirac structures and provides a rigorous answer to the question: What is the stack associated to a symplectic groupoid? The last chapter discusses a remarkable class of Poisson manifolds, called b-symplectic manifolds, giving a classification of them up to Morita equivalence and computing their Picard group.
Issue Date:2018-07-06
Type:Thesis
URI:http://hdl.handle.net/2142/101537
Rights Information:Copyright 2018 Joel Villatoro
Date Available in IDEALS:2018-09-27
Date Deposited:2018-08


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