4 papers
Hierarchies of holonomy groupoids for foliated bundles
Lachlan Ewen MacDonald
We give a new construction of the holonomy groupoid of a regular foliation in terms of a partial connection on a diffeological principal bundle of germs of transverse parametrisati…
Equivariant -theory for non-Hausdorff groupoids
Lachlan MacDonald
We give a detailed and unified survey of equivariant -theory over locally compact, second countable, locally Hausdorff groupoids. We indicate precisely how the "classical" proo…
A characteristic map for the holonomy groupoid of a foliation
Lachlan MacDonald
We prove a generalisation of Bott's vanishing theorem for the full transverse frame holonomy groupoid of any transversely orientable foliated manifold. As a consequence we obtain a…
The Godbillon-Vey invariant in equivariant -theory
Lachlan MacDonald, Adam Rennie
We construct a groupoid equivariant Kasparov class for transversely oriented foliations in all codimensions. In codimension 1 we show that the Chern character of an associated semi…