Stacks in Poisson geometry

Villatoro, Joel David

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https://hdl.handle.net/2142/101537 Copy

Description

Title

Stacks in Poisson geometry

Author(s)

Villatoro, Joel David

Issue Date

2018-07-06

Director of Research (if dissertation) or Advisor (if thesis)

Fernandes, Rui

Doctoral Committee Chair(s)

Lerman, Eugene

Committee Member(s)

• Albin, Pierre
• Pascaleff, James

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2018-08

Type of Resource

text

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

Copyright and License Information

Copyright 2018 Joel Villatoro

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