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Differentiable and algebroid cohomology, Van Est isomorphisms, and characteristic classes
Commentarii Mathematici Helvetici
In the first section we discuss Morita invariance of differentiable/algebroid cohomology. In the second section we present an extension of the van Est isomorphism to groupoids. As a first application we clarify the connection between differentiable and algebroid cohomology (proved in degree 1, and conjectured in degree 2 by Weinstein-Xu ). As a second application we extend van Est's argument for the integrability of Lie algebras. Applied to Poisson manifolds, this immediately gives a slightdoi:10.1007/s00014-001-0766-9 fatcat:c75iqyuqivbxddfll7q5fdenba