# Modular classes of Q-manifolds: a review and some applications

## TL;DR

This paper reviews the concept of modular classes in Q-manifolds, exploring their theoretical foundations and applications to structures like L-infinity algebroids and higher Poisson manifolds.

## Contribution

It provides a comprehensive review of modular classes in Q-manifolds and demonstrates their applications to advanced geometric structures.

## Key findings

- Modular class as an obstruction to Q-invariant Berezin volume
- Application to L-infinity algebroids
- Application to higher Poisson manifolds

## Abstract

A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion of the modular class of a Q-manifold -- which is viewed as the obstruction to the existence of a Q-invariant Berezin volume -- is not well know. We review the basic ideas and then apply this technology to various examples, including $L_{\infty}$-algebroids and higher Poisson manifolds.