Gauged Floer Theory Of Toric Moment Fibers



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.

Keywords and phrases

Hamiltonian displaceability Floer homology toric varieties 

2010 Mathematics Subject Classification

53D40 53D20 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Mathematics-Hill CenterRutgers UniversityPiscatawayUSA

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