This work reveals properties of open-closed maps in Hochschild and cyclic homology, suggesting links to Gromov-Witten axioms for Lagrangian submanifolds.
We construct open-closed maps on various versions of Hochschild and cyclic homology of the Fukaya A_∞ algebra of a Lagrangian submanifold modeled on differential forms. The A_∞ algebra may be curved. Properties analogous to Gromov-Witten axioms are verified. The paper is written with applications in mind to gravitational descendants and obstruction theory.
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Giterman et al. (2025) studied this question.
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