Fat distributions generalise contact structures to higher corank and admit natural contactisations. In corank two, the contactisation is a circle bundle over the original manifold. In this talk, I will explain how keeping track of this bundle structure yields a homomorphism relating the higher homotopy groups of spaces of fat distributions to those of spaces of contact structures. This construction allows invariants from contact topology to detect non-trivial families of fat distributions.
As an application, we use Bourgeois’ computation in contact homology to show that certain higher homotopy groups of spaces of fat distributions contain an infinite cyclic subgroup. Our examples are defined on products of tori with complex projective spaces.
This talk is based on joint work with Eduardo Fernández (in preparation).