Address: Mathematics Research Unit, University of Luxembourg, Maison du Nombre 6, avenue de la Fonte, L-4364 Esch-sur-Alzette
E-mail: andrewjamesbruce@googlemail.com
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.
AMSclassification: primary 17B66; secondary 53D17, 57R20, 58A50.
Keywords: Q-manifolds, modular classes, characteristic classes, higher Poisson manifolds, L_{\infty }-algebroids.
DOI: 10.5817/AM2017-4-203