Year: 2014
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Institution: Chinese University of Hong Kong
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Tsinghua University
OpenAlex ID: W3025114122