Fukaya's conjecture on Witten's twisted A_\infty structures

Kaileung Chan The Chinese University of Hong Kong Naichung Conan Leung The Chinese University of Hong Kong Ziming Nikolas Ma The Chinese University of Hong Kong

Differential Geometry mathscidoc:1807.10001

50, 2017.10
Wedge product on deRham complex of a Riemannian manifold M can be pulled back to H^∗(M) 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 M. Various applications of this conjecture to mirror symmetry are also suggested by Fukaya.
Witten deformation, Morse category
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  • accepted for publication in J. D. G.
@inproceedings{kaileung2017fukaya's,
  title={Fukaya's conjecture on Witten's twisted A_\infty structures},
  author={Kaileung Chan, Naichung Conan Leung, and Ziming Nikolas Ma},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180725111437578113120},
  pages={50},
  year={2017},
}
Kaileung Chan, Naichung Conan Leung, and Ziming Nikolas Ma. Fukaya's conjecture on Witten's twisted A_\infty structures. 2017. pp.50. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180725111437578113120.
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