Questions about cobordism of symplectic and toric manifolds

1 Toric varieties are by now familiar objects in algebraic geometry, but this note is concerned with variations on that theme, and I will try to be careful about terminology. A toric variety is a kind of orbifold, and hence has mild singularities, but I will use the term toric manifold in the sense of Davis and Januszkiewicz [4]; a smooth toric variety thus has an underlying toric manifold, but toric manifolds form a slightly more general class.