Higher holonomy and iterated integrals

Abstract

We develop a method to construct representations of the homotopy $n$-groupoid of a manifold as an $n$-category by means of K.-T. Chen’s formal homology connections for any positive integer $n$. We establish a higher holonomy functor from the homotopy $n$-groupoid to a category obtained from the tensor algebra over the homology of the manifold.