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This is a Quantitative Study study.

October 12, 2025Open Access

Differential forms, open-closed maps, and Gromov-Witten axioms

Key Points

Analyses open-closed maps in the context of Hochschild and cyclic homology, enhancing understanding of algebraic structures.
Establishes connections with Gromov-Witten axioms relevant to gravitational descendants in physics and mathematics.
Incorporates the curvature of the A_infinity algebra for a more nuanced approach to Lagrangian submanifolds.
Highlights implications for obstruction theory and its applications, paving the way for further research.

Abstract

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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Cite This Study

Giterman et al. (Sun,) studied this question.

synapsesocial.com/papers/68ebffcfdef9fcb308ff2607 https://doi.org/https://doi.org/10.48550/arxiv.2509.06034