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 \(\protect \phantom {\dot {i}\!}{K^{d_{M}}}\) we start from \(C_{d_{M}}\) as the largest simplices we have are d_M-dimensional