Orbifold Kodaira–Spencer maps and closed‐string mirror symmetry for punctured Riemann surfaces

Abstract When a Weinstein manifold admits an action of a finite abelian group, we propose its mirror construction following the equivariant 2D TQFT‐type construction, and obtain as a mirror the orbifolding of the mirror of the quotient with respect to the induced dual group action. As an application, we construct an orbifold Landau–Ginzburg mirror of a punctured Riemann surface given as an abelian cover of the pair‐of‐pants, and prove its closed‐string mirror symmetry using the closed‐open map twisted by the dual group action.