Title: Parallel Transport on Higher Path Spaces via Iterated Integrals
Abstract: In this talk I will present a construction of a parallel transport on higher path spaces of a manifold via a generalization of iterated path integrals, which I call iterated integrals on membranes. I will recall K.-T. Chen's results on de Rham structure of the fundamental group and on the loop space of a manifold via iterated path integrals.
As applications, I recover Hain's result on de Rham structure on rational homotopy groups of a manifold, and I construct a de Rham structure on the higher loop spaces of a manifold.