Homology. Cohomology. de Rham Cohomology

Abstract

In 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*)