### 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 <crainic@math.uu.nl>

Ieke Moerdijk <moerdijk@math.uu.nl>