Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A brief introduction to Poisson geometry

Henrique Bursztyn

Abstract

These notes are based on an introductory minicourse on Poisson geometry given at CRM, Barcelona, in July 2022. They mostly contain foundational material, including motivating questions and key examples of Poisson structures, and highlight some recent tools and developments. The text is largely structured through exercises that lead readers to the desired conclusions, so it serves as a guided introduction to the basics of Poisson geometry.

A brief introduction to Poisson geometry

Abstract

These notes are based on an introductory minicourse on Poisson geometry given at CRM, Barcelona, in July 2022. They mostly contain foundational material, including motivating questions and key examples of Poisson structures, and highlight some recent tools and developments. The text is largely structured through exercises that lead readers to the desired conclusions, so it serves as a guided introduction to the basics of Poisson geometry.
Paper Structure (29 sections, 153 equations)

This paper contains 29 sections, 153 equations.

Table of Contents

  1. Introduction
  2. Foundations
  3. Poisson brackets
  4. Tensorial viewpoint: bivector fields
  5. The Schouten bracket
  6. The characteristic distribution
  7. Poisson, coisotropic and cosymplectic submanifolds
  8. Some Poisson invariants
  9. Examples
  10. Quotients by symmetries
  11. Linear Poisson structures I: Lie algebras
  12. Linear Poisson structures II: Lie algebroids
  13. Poisson-Lie groups and their homogeneous spaces
  14. Log-symplectic manifolds and symplectic Lie algebroids
  15. Local structure and symplectic foliation
  16. ...and 14 more sections

Theorems & Definitions (21)

  • Example 2.1
  • Example 2.2
  • Example 2.3
  • Example 2.4
  • Example 2.5
  • Example 2.6
  • Remark 2.7
  • Remark 2.8
  • Remark 3.1
  • Example 3.2
  • ...and 11 more