Generalized complex Hamiltonian torus actions: Examples and constraints

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