Gauged Floer theory of toric moment fibers

Details Gauged Floer theory of toric moment fibers Gauged Floer theory of toric moment fibers

2010-04-16

arxiv.org/abs/1004.2841v5

Mathematics

Symplectic Geometry

69 pages, 17 figures. Small corrections and improvements from the last version

Scientific paper

We investigate the small area limit of the gauged Lagrangian Floer cohomology of Frauenfelder. The resulting cohomology theory, which we call quasimap Floer cohomology, is an obstruction to displaceability of Lagrangians in the symplectic quotient. We use the theory to reproduce the results of Fukaya-Oh-Ohta-Ono and Cho-Oh on non-displaceability of moment fibers of not-necessarily-Fano toric varieties and extend their results to toric orbifolds, without virtual fundamental chains. Finally we describe a conjectural relationship to Floer cohomology in the quotient.

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