Tuesday, June 19, 2012

1206.3994 (Cheol-Hyun Cho et al.)

Holomorphic orbidiscs and Lagrangian Floer cohomology of symplectic
toric orbifolds

Cheol-Hyun Cho, Mainak Poddar
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.
View original: http://arxiv.org/abs/1206.3994

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