Multiplicative structures over convergent Novikov rings in equivariant Floer theory

Develop a convergent Novikov-ring-based framework for defining multiplicative structures in LG-equivariant Floer theory of compact Hamiltonian G-manifolds, analogous to the anticipated additive constructions that rely on virtual fundamental classes.

Background

The authors discuss the limitations of working over formal Novikov rings, which can obscure trapped sectors and analytic variation. They expect that additive LG-equivariant Floer complexes can be defined over convergent Novikov rings using virtual fundamental classes.

However, they point out that an analogue for multiplicative structures in this convergent setting is not presently available.