English

Chern-Simons theory and string topology

Algebraic Topology 2023-12-12 v1

Abstract

We construct chain-level S1S^1-equivariant string topology for each simply connected closed manifold. This amounts to constructing a Maurer-Cartan element for the canonical involutive Lie bialgebra (IBL) structure on the dual cyclic bar complex of its de Rham cohomology which is unique up to IBL{\rm IBL}_\infty gauge equivalence. The construction involves integrals over configuration spaces associated to trivalent ribbon graphs, which can be seen as a version of perturbative Chern-Simons theory in arbitrary dimension.

Keywords

Cite

@article{arxiv.2312.05922,
  title  = {Chern-Simons theory and string topology},
  author = {Kai Cieliebak and Evgeny Volkov},
  journal= {arXiv preprint arXiv:2312.05922},
  year   = {2023}
}
R2 v1 2026-06-28T13:46:24.670Z