Journal of Differential Geometry

Holomorphic orbi-discs and Lagrangian Floer cohomology of symplectic toric orbifolds

Cheol-Hyun Cho and Mainak Poddar

Full-text: Open access

Abstract

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.

Article information

Source
J. Differential Geom., Volume 98, Number 1 (2014), 21-116.

Dates
First available in Project Euclid: 23 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1406137695

Digital Object Identifier
doi:10.4310/jdg/1406137695

Mathematical Reviews number (MathSciNet)
MR3263515

Zentralblatt MATH identifier
1300.53077

Citation

Cho, Cheol-Hyun; Poddar, Mainak. Holomorphic orbi-discs and Lagrangian Floer cohomology of symplectic toric orbifolds. J. Differential Geom. 98 (2014), no. 1, 21--116. doi:10.4310/jdg/1406137695. https://projecteuclid.org/euclid.jdg/1406137695


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