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 S1-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.
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