Products of topological amplitudes: an algebraic solution

Given topological amplitudes with specific genus and boundary structure the authors define a product of these amplitudes, also specified by a genus and a boundary structure. It is shown that this product is independent of the particular graphical representation of the members of the product; an explicit construction to obtain the boundary structure of this product without using graphs is described, and finally the general formula to compute the genus of the product is derived. (Auth.)