15 citations · 34 across the 14 of their papers we have counts for
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Chern-Weil theory for Haefliger-singular foliations
Lachlan Ewen MacDonald, Benjamin McMillan
We give a Chern-Weil map for the Gel'fand-Fuks characteristic classes of Haefliger-singular foliations, those foliations defined by smooth Haefliger structures with dense regular s…
On the Chern character in Higher Twisted K-theory and spherical T-duality
Lachlan Macdonald, Varghese Mathai, Hemanth Saratchandran
In this paper, we construct for higher twists that arise from cohomotopy classes, the Chern character in higher twisted K-theory, that maps into higher twisted cohomology. We show…
The Holonomy Groupoids of Singularly Foliated Bundles
Lachlan Ewen MacDonald
We define a notion of connection in a fibre bundle that is compatible with a singular foliation of the base. Fibre bundles equipped with such connections are in plentiful supply, a…
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…
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…