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arXiv · 2004.06162

The transverse density bundle and modular classes of Lie groupoids

Marius Crainic·João Nuno Mestre
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Abstract

In this note we revisit the notions of transverse density bundle and of modular classes of Lie algebroids and Lie groupoids; in particular, we point out that one should use the transverse density bundle $\mathcal{D}_{A}^{\textrm{tr}}$ instead of $Q_A$, which is the representation that is commonly used when talking about modular classes. One of the reasons for this is that, as we will see, $Q_A$ is not really an object associated to the stack presented by a Lie groupoid (in general, it is not a representation of the groupoid!).

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Marius Crainic, João Nuno Mestre. 2020-04-13. The transverse density bundle and modular classes of Lie groupoids. https://arxiv.org/abs/2004.06162

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