Deformations of Vector Bundles over Lie Groupoids
Differential Geometry
2019-07-15 v1 Representation Theory
Symplectic Geometry
Abstract
VB-groupoids are vector bundles in the category of Lie groupoids. They encompass several classical objects, including Lie group representations and 2-vector spaces. Moreover, they provide geometric pictures for 2-term representations up to homotopy of Lie groupoids. We attach to every VB-groupoid a cochain complex controlling its deformations and discuss its fundamental features, such as Morita invariance and a van Est theorem. Several examples and applications are given.
Cite
@article{arxiv.1907.05670,
title = {Deformations of Vector Bundles over Lie Groupoids},
author = {Pier Paolo La Pastina and Luca Vitagliano},
journal= {arXiv preprint arXiv:1907.05670},
year = {2019}
}
Comments
39 pages. Comments welcome!!