Ezra Getzler: Cubical methods and higher Lie groupoids

Abstract

We construct the higher Lie groupoid associated to a differential groupoid using the de Rham theorem for cubical sets. The de Rham theorem for cubical sets seems to have a lower degree of computational complexity compared to the de Rham theorem for simplicial sets - this is a key theme of this talk.

Using a result of Berglund (the homological perturbation lemma for dg Lie algebras), we construct a higher dimensional analogue of holonomy (path ordered exponential in the one-dimensional case), which seems to encompass all previous definitions.