Q-groupoids and their cohomology

Details Q-groupoids and their cohomology Q-groupoids and their cohomology

2006-11-29

arxiv.org/abs/math/0611924v2

Pacific Journal of Mathematics 242 (2009), no. 2, 311-332

Mathematics

Differential Geometry

v2 is the published version. Significant revision over previous version, particularly in section 5.2

Scientific paper

10.2140/pjm.2009.242.311

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".

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