Radon invariance of microlocal perverse schobers

Establish an equivalence between the categories of localized microlocal perverse schobers associated with any pair of dual non-characteristic families of discs under the affine Radon transform, namely between the categories associated with a hypersurface family H in the coordinates (x,y) and its dual family \check{H} in the coordinates (a,b).

Background

The paper develops localized microlocal perverse schobers by categorifying the local Gelfand–MacPherson–Vilonen construction. For perverse sheaves, the corresponding quotient categories are invariant under the Radon transform induced by the contact identification between the relevant cosphere bundles.

The proposed categorified theory is shown to satisfy the conjecture at the level of equivalence classes of objects for the torus singularities y^m=x^n. The full categorical equivalence for general dual non-characteristic families remains unresolved.