Constraints for topological strings in D≥1

New relations of correlation functions are found in topological string theory; one for each second cohomology class of the target space. They are close cousins of the Deligne-Dijkgraaf-Witten's puncture and dilaton equations. When combined with the dilaton equation and ghost number conservation, the equation for the first Chern class of the target space gives a constraint on the topological sum (over genera and (multi-)degrees) of partition functions. For the bfCP1 model, it coincides with the dilatation constraint which is derivable in the matrix model recently introduced by Eguchi and Yang. ((orig.))