Differential forms with values in VB-groupoids
Differential Geometry
2021-09-15 v1
Abstract
We introduce multiplicative differential forms on Lie groupoids with values in VB-groupoids. Our main result gives a complete description of these objects in terms of infinitesimal data. By considering split VB-groupoids, we are able to present a Lie theory for differential forms on Lie groupoids with values in 2-term representations up to homotopy. We also define a differential complex whose 1-cocycles are exactly the multiplicative forms with values in VB-groupoids and study the Morita invariance of its cohomology.
Cite
@article{arxiv.1804.05289,
title = {Differential forms with values in VB-groupoids},
author = {Thiago Drummond and Leandro Egea},
journal= {arXiv preprint arXiv:1804.05289},
year = {2021}
}
Comments
36 pages