Journal of Symplectic Geometry

Volume 20 (2022)

Number 4

Twisted cyclic group actions on Fukaya categories and mirror symmetry

Pages: 813 – 835

DOI: https://dx.doi.org/10.4310/JSG.2022.v20.n4.a2

Authors

Chi Hong Chow (Institute of Mathematical Sciences and Department of Mathematics, Chinese University of Hong Kong)

Naichung Conan Leung (Institute of Mathematical Sciences and Department of Mathematics, Chinese University of Hong Kong)

Abstract

Let $(X, \omega)$ be a compact symplectic manifold whose first Chern class $c_1(X)$ is divisible by a positive integer $n$. We construct a twisted $\mathbb{Z}_{2n}$-action on its Fukaya category $Fuk(X)$ and a $\mathbb{Z}_n$-action on the local models of its moduli of Lagrangian branes. We show that this action is compatible with the gluing functions for different local models.

Received 8 June 2021

Accepted 7 October 2021

Published 16 March 2023