Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey

TL;DR

This survey reviews the properties of Poisson manifolds and Lie algebroids, focusing on recent developments in modular classes, including their applications to twisted structures and the spinor approach.

Contribution

It provides a comprehensive overview of recent research on modular classes in various Poisson and Lie algebroid structures, highlighting new insights and methods.

Findings

Summary of properties of Poisson manifolds and Lie algebroids

Recent advances in modular classes of Poisson and twisted Poisson manifolds

Introduction to the spinor approach to modular classes

Abstract

After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of Poisson-Nijenhuis manifolds. A review of the spinor approach to the modular class concludes the paper.