Generalized complex hamiltonian torus actions: Examples and constraints

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 $rank(T)\le n-2$ 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.