Geodesic
Modular classes of Q-manifolds: a review and some applications
Archivum mathematicum, Tome 53 (2017) no. 4, pp. 203-219

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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.
DOI : 10.5817/AM2017-4-203
Classification : 17B66, 53D17, 57R20, 58A50
Keywords: Q-manifolds; modular classes; characteristic classes; higher Poisson manifolds; $L_{\infty }$-algebroids 
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Bruce, Andrew James. Modular classes of Q-manifolds: a review and some applications. Archivum mathematicum, Tome 53 (2017) no. 4, pp. 203-219. doi: 10.5817/AM2017-4-203

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