Open FJRW theory and mirror symmetry
Abstract
We construct an open enumerative theory for the Landau-Ginzburg (LG) model .C 2 ; r s ; x r C y s /.The invariants are defined as integrals of multisections of a Witten bundle with descendents over a moduli space that is a real orbifold with corners.In turn, a generating function for these open invariants yields the mirror LG model and a versal deformation of it with flat coordinates.After establishing an open topological recursion result, we prove an LG/LG open mirror symmetry theorem in dimension two with all descendents.The open invariants we define are not unique but depend on boundary conditions that, when altered, exhibit wall-crossing phenomena for the invariants.We describe an LG wall-crossing group classifying the wall-crossing transformations that can occur.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Nonlinear Waves and Solitons
Advanced Algebra and Geometry
Publication details
- Journal / source
- Geometry & Topology
- Publisher
- Mathematical Sciences Publishers
- Volume
- 30
- Issue
- 8
- Pages
- 2779–2960
- Publication date
- 30 August 2026
- Language
- EN