Fig. 5.

Chains, cycles and boundaries sets and their maps under the boundary operator for the d-skeleton of a complex K, with d=d_M. C_d, Z_d and B_d represent the collections of d chains, cycles and boundaries respectively. Notice that in K we may well have C_d+1 and bigger dimensional chains with corresponding boundary operators, while in $K^{d_M}$ we start from $C_{d_M}$ as the largest simplices we have are d_M-dimensional