Explicit multiplicative splittings of the trapped short exact sequence

Construct explicit multiplicative splittings of the short exact sequence 0 → tHF^*_LG(X) → QH^*_LG(X) → A^*(X//G) → 0 relating LG-equivariant quantum cohomology, the trapped Floer cohomology ideal, and the additive quotient algebra, for compact Hamiltonian G-manifolds X.

Background

Theorem 2 produces an exact sequence expressing the additive quotient from the LG-equivariant quantum cohomology of X to an algebra A^*(X//G), with kernel the trapped ideal tHF^*_LG(X).

While specific examples admit multiplicative splittings (e.g., in Iritani’s blow-up work), a general explicit multiplicative splitting is not known.