I recently found out about Chen's iterated integrals for paths in a differentiable manifold, and I was wondering if an analogous construction exists for free loops, i.e. a set of v …

I have encountered iterated integrals on papers dealing with multizeta values, polylogarithms etc.. Since then I am trying to figure out the motivations and purpose of the theory. …

For a smooth manifold $X$, let $B_s(X)$ denote the space of iterated integrals of length at most $s$. Here we consider iterated integrals as functions on the path space $PX$. Fix a …