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Homology. Cohomology. de Rham Cohomology
1997In mathematics one often encounters the following situation. Let a sequence of abelian groups (modules) ... be given $$ \{ {C^n},n \in \mathbb{Z}\} $$ (1*) together with homomorphisms d n : C n → C n+1 (called differentials or coboundary homomorphisms) for whose $$ {d_{n + 1}}{d_n} = 0 (zero group) for all n. $$ (2*)
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