Application of parallel transport on loop spaces to gravity

Abstract: A new notion of parallel transport on loop spaces via iterated integrals is emerging in algebraic topology. I will apply such ideas to gravity and draw a parallel will electromagnetism (in 3+1 dimensions). As an application to gravity, I will present an analogue of the Riemann curvature tensor as an iterated integral over a path space. We propose an interpretation of this analogue in terms of homotopy and uncertainty.