Principal actions of stacky Lie groupoids
Differential Geometry
2018-06-07 v2 Category Theory
Abstract
Stacky Lie groupoids are generalizations of Lie groupoids in which the "space of arrows" of the groupoid is a differentiable stack. In this paper, we consider actions of stacky Lie groupoids on differentiable stacks and their associated quotients. We provide a characterization of principal actions of stacky Lie groupoids, i.e., actions whose quotients are again differentiable stacks in such a way that the projection onto the quotient is a principal bundle. As an application, we extend the notion of Morita equivalence of Lie groupoids to the realm of stacky Lie groupoids, providing examples that naturally arise from non-integrable Lie algebroids.
Cite
@article{arxiv.1510.09208,
title = {Principal actions of stacky Lie groupoids},
author = {Henrique Bursztyn and Francesco Noseda and Chenchang Zhu},
journal= {arXiv preprint arXiv:1510.09208},
year = {2018}
}
Comments
80 pages. v.2: new introduction. A shortened version of this paper is accepted at IMRN