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Chern-Simons theory and string topology
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Chern-Simons theory and string topology
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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.
Forward citations
Cited by 3 Pith papers
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String topology operations under Chen's iterated integrals and homotopy transfer
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.
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A cord algebra for tori in three-space
A cord algebra is defined for tori surrounding knots and identified with the knot cord algebra, indirectly relating it to Legendrian contact homology of the unit conormal bundle.
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Calabi-Yau Deformation Quantization
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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