Fukaya's conjecture on Witten's twisted $A_\infty$-structures
Differential Geometry
2020-05-18 v5 Analysis of PDEs
Abstract
Wedge product on deRham complex of a Riemannian manifold can be pulled back to via explicit homotopy, constructed using Green's operator, to give higher product structures. We prove Fukaya's conjecture which suggests that Witten deformation of these higher product structures have semiclassical limits as operators defined by counting gradient flow trees with respect to Morse functions, which generalizes the remarkable Witten deformation of deRham differential from a statement concerning homology to one concerning real homotopy type of . Various applications of this conjecture to mirror symmetry are also suggested by Fukaya.
Cite
@article{arxiv.1401.5867,
title = {Fukaya's conjecture on Witten's twisted $A_\infty$-structures},
author = {Kaileung Chan and Naichung Conan Leung and Ziming Nikolas Ma},
journal= {arXiv preprint arXiv:1401.5867},
year = {2020}
}