  The scalar and vector topological Yang-Mills symmetries on Calabi-Yau
manifolds geometrically define consistent sectors of Yang-Mills D=4,6 N=1
supersymmetry, which fully determine the supersymmetric actions up to twist.
For a CY_2 manifold, both N=1,D=4 Wess and Zumino and superYang-Mills theory
can be reconstructed in this way. A superpotential can be introduced for the
matter sector, as well as the Fayet-Iliopoulos mechanism. For a CY_3 manifold,
the N=1, D=6 Yang-Mills theory is also obtained, in a twisted form. Putting
these results together with those already known for the D=4,8 N=2 cases, we
conclude that all Yang--Mills supersymmetries with 4, 8 and 16 generators are
determined from topological symmetry on special manifolds.
