Definition. Boundary homomorphism (also known as differential) [EFJB]

The boundary homomorphism $\partial_n : C^\Delta_n(X) \to C^\Delta_{n-1}(X)$Definition$n$-th simplicial chain module and $n$-chains2026-10-04 · Lîm Tsú-thuàn for $n \ge 1$ is defined on the basis by

i.e. Alternatively add each restriction $\sigma^n_\alpha\vert_{[v_0, \dots, \widehat{v}_i, \dots, v_n]}$. Recall the third condition of $\Delta$-complexDefinitionDelta complex2026-10-04 · Lîm Tsú-thuàn.