Helicity as a Foliated Cobordism Invariant 1

Helicity is an invariant of smooth volume-preserving vector fields on a 3-manifold. Arnold asked whether helicity admits an extension to 𝐶0 volume-preserving flows. In previous work, we constructed such an extension for a large class of 𝐶0 flows.

In these talks, we explain a geometric interpretation of helicity as a foliated cobordism invariant, both in the smooth and 𝐶0 settings. Based on joint work with Oliver Edtmair.