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July 2021 Fukaya’s conjecture on Witten’s twisted $A_\infty$ structure
Kaileung Chan, Naichung Conan Leung, Ziming Nikolas Ma
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J. Differential Geom. 118(3): 399-455 (July 2021). DOI: 10.4310/jdg/1625860622

Abstract

The wedge product on de Rham complex of a Riemannian manifold $M$ can be pulled back to $H^\ast (M)$ via explicit homotopy constructed by using Green’s operator which gives higher product structures. We prove Fukaya’s conjecture which suggests that Witten deformation of these higher product structures has semiclassical limits as operators defined by counting gradient flow trees with respect to Morse functions, which generalizes the remarkable Witten deformation of de Rham differential from a statement concerning homology to one concerning real homotopy type of $M$. Various applications of this conjecture to mirror symmetry are also suggested by Fukaya in [6].

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Kaileung Chan. Naichung Conan Leung. Ziming Nikolas Ma. "Fukaya’s conjecture on Witten’s twisted $A_\infty$ structure." J. Differential Geom. 118 (3) 399 - 455, July 2021. https://doi.org/10.4310/jdg/1625860622

Information

Received: 13 September 2017; Accepted: 12 September 2019; Published: July 2021
First available in Project Euclid: 10 July 2021

Digital Object Identifier: 10.4310/jdg/1625860622

Rights: Copyright © 2021 Lehigh University

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Vol.118 • No. 3 • July 2021
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