Guangbo Xu's Seminar

In Hamiltonian Floer theory one needs to regularize infinitely many moduli spaces. It is convenient to formalize the discussion using the language of flow categories and bimodules. In this lecture I will explain how to use the notion of "derived orbifold chart lift" of flow categories and bimodules and the FOP perturbation scheme to define chain complexes and chain maps over the integers. In the context of Arnold conjecture, I will explain how the necessary structures on the derived orbifold chart lifts for the Hamiltonian Floer flow category and the PSS/SSP bimodules can be constructed. This lecture is based on the joint work with S. Bai (arXiv: 2209.08599).