The transverse density bundle and modular classes of Lie groupoids
Differential Geometry
2020-04-15 v1
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 instead of , 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, is not really an object associated to the stack presented by a Lie groupoid (in general, it is not a representation of the groupoid!).
Cite
@article{arxiv.2004.06162,
title = {The transverse density bundle and modular classes of Lie groupoids},
author = {Marius Crainic and João Nuno Mestre},
journal= {arXiv preprint arXiv:2004.06162},
year = {2020}
}
Comments
8 pages; this note is an expanded version of a section which had appeared in the first version of arXiv:1603.01673 [math.DG]