2012/06/21 by Cheol-Hyun Cho, Mainak Poddar · 2 citations
Mathematics · Physics and Astronomy · #math.SG #math-ph #math.MP #msc:53D12 #msc:53D40
published as J. Differential Geom. Volume 98, Number 1 (2014), 21-116 · 75 pages, 4 figures. shortened by reducing repetition of construction from manifold cases
arxiv created 2012/06/21 · arxiv updated 2014/08/01
We develop Floer theory of Lagrangian torus fibers in compact symplectic toric orbifolds. We first classify holomorphic orbi-discs with boundary on Lagrangian torus fibers. We show that there exists a class of basic discs such that we have one-to-one correspondences between a) smooth basic discs and facets of the moment polytope, and b) between basic orbi-discs and twisted sectors of the toric orbifold. We show that there is a smooth Lagrangian Floer theory of these torus fibers, which has a bulk-deformation by fundamental classes of twisted sectors of the toric orbifold. We show by several examples that such bulk-deformation can be used to illustrate the very rigid Hamiltonian geometry of orbifolds. We define its potential and bulk-deformed potential, and develop the notion of leading order potential. We study leading term equations analogous to the case of toric manifolds by Fukaya, Oh, Ohta and Ono.