Differential forms with values in VB-groupoids
arXiv:1804.05289 · doi:10.1016/j.geomphys.2018.08.019
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.
arXiv comment36 pages
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Cited by in corpus (7)
- Lie theory of multiplicative tensors
- Infinitesimal Automorphisms of VB-groupoids and algebroids
- Contact Dual Pairs
- Local formulas for multiplicative forms
- Integrating Nijenhuis Structures
- Atiyah sequences and connections on principal bundles over differentiable stacks
- Local and global integrability of Lie brackets