Quasimap Floer cohomology and varying symplectic quotients

TL;DR

This paper employs quasimap Floer cohomology to analyze the displaceability of toric moment fibers in varying symplectic quotients, revealing new non-displaceable fibers and clarifying displaceability in symplectic ellipsoids.

Contribution

It introduces a novel application of quasimap Floer cohomology to study displaceability in symplectic quotients, addressing longstanding questions and providing new examples.

Findings

Identified an open subset of non-displaceable toric fibers with a codimension four singular set.

Determined displaceability for most fibers of a symplectic ellipsoid.

Partially answered a question of McDuff regarding non-displaceable orbits.

Abstract

We use quasimap Floer cohomology for varying symplectic quotients to resolve several puzzles regarding displaceability of toric moment fibers. For example, we (i) present a compact Hamiltonian torus action containing an {\em open} subset of non-displaceable orbits and a codimension four singular set, partly answering a question of McDuff, and (ii) determine displaceability for most of the moment fibers of a symplectic ellipsoid.