Stacks in Poisson geometry

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Villatoro, Joel David

Contributors dc:contributor

• Fernandes, Rui
• Lerman, Eugene
• Albin, Pierre
• Pascaleff, James

• Stacks, Differential Manifolds, Poisson Manifolds, Symplectic Manifolds.

Statement dc:rights

• Copyright 2018 Joel Villatoro

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101537

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101537