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

Andrew James Bruce (2017)

Archivum Mathematicum

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 -algebroids and higher Poisson manifolds.

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