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

Kai Cieliebak; Evgeny Volkov

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

Differential Geometry 2026-07-04 v1 Algebraic Topology

Authors: Kai Cieliebak , Evgeny Volkov

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.

Cite

@article{arxiv.2607.03782,
  title  = {String topology operations under Chen's iterated integrals and homotopy transfer},
  author = {Kai Cieliebak and Evgeny Volkov},
  journal= {arXiv preprint arXiv:2607.03782},
  year   = {2026}
}

Comments

126 pages, 11 figures