A brief introduction to Poisson geometry

TL;DR

This paper provides a foundational introduction to Poisson geometry, covering key concepts, examples, and recent developments, aimed at guiding readers through essential ideas and tools in the field.

Contribution

It offers an accessible, exercise-based overview of Poisson geometry, emphasizing recent tools and developments for beginners and researchers.

Findings

Introduction to key Poisson structures and examples

Highlighting recent tools and methods in Poisson geometry

Structured through exercises for guided learning

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.