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Deformation Theory Seminar

Wednesday, April 5, 2017 - 2:00pm

Ivan Horozov



University of Pennsylvania


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.