Chern-Simons theory and string topology
Algebraic Topology
2023-12-12 v1
Abstract
We construct chain-level -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 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}
}