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

Kai Cieliebak; Evgeny Volkov

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arXiv · 2607.03782

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

Kai Cieliebak·Evgeny Volkov

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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.

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Kai Cieliebak, Evgeny Volkov. 2026-07-04. String topology operations under Chen's iterated integrals and homotopy transfer. https://arxiv.org/abs/2607.03782

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