Chern-Simons theory and string topology

Kai Cieliebak; Evgeny Volkov

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arXiv · 2312.05922

Chern-Simons theory and string topology

Kai Cieliebak·Evgeny Volkov

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Abstract

We construct chain-level $S^1$-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 ${\rm IBL}_\infty$ 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.

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BibTeX RIS

Kai Cieliebak, Evgeny Volkov. 2023-12-10. Chern-Simons theory and string topology. https://arxiv.org/abs/2312.05922

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