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Gauged Floer Theory Of Toric Moment Fibers

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Abstract

We investigate the small area limit of the gauged Lagrangian Floer cohomology of Frauenfelder [Fr1]. 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 [FuOOO3,1] and Cho–Oh [CO] on non-displaceability of moment fibers of not-necessarily-Fano toric varieties and extend their results to toric orbifolds, without using virtual fundamental chains. Finally, we describe a conjectural relationship with Floer cohomology in the quotient.

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  1. Mathematics-Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA

    Christopher T. Woodward

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Partially supported by NSF grant DMS0904358

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Woodward, C.T. Gauged Floer Theory Of Toric Moment Fibers. Geom. Funct. Anal. 21, 680–749 (2011). https://doi.org/10.1007/s00039-011-0119-6

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