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Chain-level equivariant string topology: algebra versus analysis
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Chain-level equivariant string topology: algebra versus analysis
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We prove that on 2-connected closed oriented manifolds, the analytic and algebraic constructions of an IBL$_\infty$ structure associated to a closed oriented manifold coincide. The corresponding structure is invariant under orientation preserving homotopy equivalences and induces on homology the involutive Lie bialgebra structure of Chas and Sullivan.
Forward citations
Cited by 2 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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Minimal Unital Cyclic $C_\infty$-Algebras and the Real and Rational Homotopy Type of Closed Manifolds
For (r−1)-connected closed manifolds of dimension n ≤ l(r−1)+2, rational homotopy type is determined by the cohomology ring and the minimal cyclic C∞-algebra enhancement up to isotopy modulo l−2.
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