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

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.

11 pages. Comments are welcomed

References in corpus (3)

• $Q$-Manifolds and Mackenzie Theory
• Q-manifolds and Mackenzie theory: an overview
• Unimodular L-infinity algebras