where the rank of enumeration E m,n coincide with the group actions Γ = Z n . Intuitively speaking, one can do a gluing surgery by inserting periodic boundary condition on any n-hypercube in K. It indicates that transfer homomorphism acting on a linear space (chain complexes) with countable basis has a kernel rank{ker p # (C m (K))} = n m as characteristic of Z can be regarded as either 0 or Z without confusion. Since