String topology operations under Chen's iterated integrals and homotopy transfer

Abstract

We develop the analytical foundations for integrals over configuration spaces used to relate chain-level $S^1$-equivariant string topology to perturbative Chern-Simons theory. As an application, we prove that the composition of Chen's iterated integral with homotopy transfer intertwines the involutive Lie bialgebra structures on homology.

126 pages, 11 figures