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.

arXiv comment11 pages. Comments are welcomed

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Cited by in corpus (2)

• Homological sections of Lie algebroids
• Modular Classes of Q-Manifolds, Part II: Riemannian Structures & Odd Killing Vectors Fields