  Consider an effective Hamiltonian torus action $T\times M \to M$ on a
topologically twisted,generalized complex manifold $M$ of dimension $2n$. We
prove that the $rank(T) \leq n-2$ and that the topological twisting survives
Hamiltonian reduction. We then construct a large new class of such actions
satisfying $rank(T) = n-2$, using a surgery procedure on toric manifolds.
