Wall-crossing for invariants of equivariant 3CY categories

We provide a wall-crossing framework for operational enumerative invariants of equivariant 3-Calabi–Yau categories arising from virtual cycles. The strategy follows ideas of Joyce’s ``universal’’ wall-crossing framework arXiv:2111.04694, using the authors’ symmetrized pullback technique to preserve the symmetry of the (almost-perfect) obstruction theories throughout. As an application, we define and study wall-crossings of simple type between operational equivariant Donaldson–Thomas (DT), Pandharipande–Thomas (PT), and Bryan–Steinberg (BS) vertices. In particular, we give an explicit DT/PT descendent vertex correspondence in the Calabi–Yau limit. As another application, we construct and prove wall-crossing formulas for operational refined semistable Vafa–Witten invariants.