Q-groupoids and their cohomology
Differential Geometry
2011-10-19 v2 Symplectic Geometry
Abstract
We approach Mackenzie's LA-groupoids from a supergeometric point of view by introducing Q-groupoids, which are groupoid objects in the category of Q-manifolds. There is a faithful functor from the category of LA-groupoids to the category of Q-groupoids. We associate to every Q-groupoid a double complex that provides a model for the Q-cohomology of the classifying space. As examples, we obtain models for equivariant Q- and orbifold Q-cohomology, and for equivariant Lie algebroid and orbifold Lie algebroid cohomology. We obtain double complexes associated to Poisson groupoids and groupoid-algebroid "matched pairs".
Cite
@article{arxiv.math/0611924,
title = {Q-groupoids and their cohomology},
author = {Rajan Amit Mehta},
journal= {arXiv preprint arXiv:math/0611924},
year = {2011}
}
Comments
v2 is the published version. Significant revision over previous version, particularly in section 5.2