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

When a Weinstein manifold admits an action of a finite abelian group, we propose its mirror construction following the equivariant 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 (part of) closed-open map twisted by the dual group action.