Foliation groupoids and their cyclic homology, by Marius Crainic and Ieke Moerdijk

Our first theorem provides a criterion for determining whether a given Lie groupoid is equivalent to an \'etale one. We prove that this is the case iff all the isotropy groups of the groupoid are discrete, or equivalently, iff the groupoid integrates a foliation. These groupoids are called ``foliation groupoids''. We also show that the holonomy and the monodromy groupoids are extreme examples of foliation groupoids. The last theorem asserts that equivalent foliation groupoids have isomorphic Hochschild, cyclic and periodic cyclic homology groups.

Marius Crainic <>
Ieke Moerdijk <>