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Pseudodifferential calculus on a singular foliation
Iakovos Androulidakis, Georges Skandalis
In a previous paper ([1]), we associated a holonomy groupoid and a C*-algebra to any singular foliation (M,F). Using these, we construct the associated pseudodifferential calculus.…
The holonomy groupoid of a singular foliation
Iakovos Androulidakis, Georges Skandalis
We construct the holonomy groupoid of any singular foliation. In the regular case this groupoid coincides with the usual holonomy groupoid of Winkelnkemper (1983); the same holds i…
Crossed modules and the integrability of Lie brackets
Iakovos Androulidakis
We show that the integrability obstruction of a transitive Lie algebroid coincides with the lifting obstruction of a crossed module of groupoids associated naturally with the given…
Classification of extensions of principal bundles and transitive Lie groupoids with prescribed kernel and cokernel
Iakovos Androulidakis
The equivalence of principal bundles with transitive Lie groupoids due to Ehresmann is a well known result. A remarkable generalisation of this equivalence, due to Mackenzie, is th…
On the connection theory of transitive Lie groupoids
Iakovos Androulidakis
Due to a result by Mackenzie, extensions of transitive Lie groupoids are equivalent to certain Lie groupoids which admit an action of a Lie group. This paper is a treatment of the…