  There is a description of the torsion product of two modules in terms of
generators and relations given by Eilenberg and Mac Lane. With some additional
data on the chain complexes there is a splitting of the map in the Kunneth
formula in terms of these generators. Different choices of this additional data
determine a natural coset reminiscent of the indeterminacy in a Massey triple
product. In one class of examples the coset actually is a Massey triple
product.
  The explicit formulas for a splitting enable proofs of results on the
behavior of the interchange map and the long exact sequence boundary map on all
the terms in the Kunneth formula. Information on the failure of naturality of
the splitting is also obtained.
