20250620 Anna Fokma

Holonomic approximation is the main tool used in proving that the h-principle holds on open manifolds for a large class of partial differential relations. In the first part of this talk I discuss a generalization of holonomic approximation which also works on closed manifolds, using mild singularities known as wrinkles. In the second part, we use this result to carry out the first step of a strategy proposed by Laudenbach and Meigniez to study h-principles via a certain type of singular foliations known as Haefliger structures. We end with an application to the classifying space of principal groupoid bundles which encode Haefliger structures with a transverse geometry.