Fixed-point localization description of the trapped Floer cohomology ideal

Determine an explicit description, in terms of fixed-point localization data for the Hamiltonian G-action on X, of the LG-equivariant trapped Floer cohomology ideal tHF^*_LG(X) defined by classes that stop at critical sets under Floer continuation by the Hamiltonians Kµ.

Background

In non-anticanonical or non-monotone settings, the authors identify an ideal of ‘trapped cohomology’ tHF^*_LG(X) consisting of Floer classes that are unable to pass through critical loci under continuation by Kµ. This ideal is the kernel in the additive description of the quotient leading to X//G.

They connect the phenomenon to symplectic cohomology with supports and to recent work of Varolgunes and collaborators; however, a characterization via fixed-point localization on X is currently missing.