GDO

Abstract

I will explain why the Sullivan simplicial set given by a differential non-negatively graded manifold is actually a Kan simplicial manifold. The basic tool is an integral transformation that linearizes the corresponding PDE. By imposing a gauge condition, we can then locally find a finite-dimensional Kan submanifold, which can be seen as a local Lie n-groupoid integrating the dg manifold. These local n-groupoids are (non-uniquely) isomorphic on the overlaps. I will mention many open problems. Based on a joint work in progress with Michal Siran.