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Chern-Simons theory and string topology

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arxiv 2312.05922 v2 pith:ARQ626ZX submitted 2023-12-10 math.AT

Kai Cieliebak , Evgeny Volkov This is my paper · ORCID
classification math.AT
keywords chern-simonsstringtheorytopologyamountsarbitraryassociatedbialgebra
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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

    math.DG 2026-07 accept novelty 6.0 of 10

    Chen iterated integrals plus homotopy transfer intertwine the involutive Lie bialgebra of S1-equivariant string topology with the IBL operations on the dual cyclic bar complex of a harmonic subspace.

  2. The Batalin-Vilkovisky formalism in noncommutative effective field theory

    math.QA 2025-05 conditional novelty 6.0 of 10

    The paper establishes the BV quantization formalism for noncommutative effective field theories, proves compatibility of the quantum master equation with the renormalization group flow, and quantizes a noncommutative ...

  3. Calabi-Yau Deformation Quantization

    math.QA 2026-07 conditional novelty 3.0 of 10

    A Calabi-Yau version of Kontsevich's formality morphism is recorded, yielding canonical closed deformation quantizations for unimodular holomorphic Poisson Calabi-Yau manifolds.

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