We compute the contour integral for the partition function of an \( \mathcal{N} \) = 2 SU(2) topologically twisted theory on \( {\mathbbm{CP}}^2 \) , dimensionally reducing from an \( \mathcal{N} \) = 1 theory on S5. Earlier works presented the partition function as a sum over three equivariant fluxes, one for each toric divisor of \( {\mathbbm{CP}}^2 \) . Our result depends only on a single physical flux, assigned to the non-trivial two-cycle of the manifold. The reduced summation over fluxes is compensated by a contour of integration, arising from a different solution of the BPS equations, which captures more poles in each topological sector. As our observable involves a position-dependent Yang-Mills coupling, we compute new equivariant invariants of \( {\mathbbm{CP}}^2 \) , which reduce to Donaldson invariants in the non-equivariant limit. Stability conditions of gauge bundles over \( {\mathbbm{CP}}^2 \) appear intrinsically via the dimensional reduction.
