Geometric and Functional Analysis

, 21:680

Gauged Floer Theory Of Toric Moment Fibers

Article

DOI: 10.1007/s00039-011-0119-6

Cite this article as:
Woodward, C.T. Geom. Funct. Anal. (2011) 21: 680. doi:10.1007/s00039-011-0119-6

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.

Keywords and phrases

Hamiltonian displaceabilityFloer homologytoric varieties

2010 Mathematics Subject Classification

53D4053D20

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Mathematics-Hill CenterRutgers UniversityPiscatawayUSA