On cohomologies of double complexes. (Russian) Zbl 0906.55014

Gorinov, A. G.

Vestn. Mosk. Univ., Ser. I 1997, No. 5, 54-56 (1997).

Let \(C^{**} = (C^{p,q})_{p,q\in{\mathbb Z}}\) be a double complex. The author proves that any two complexes \(C^*_1\) and \(C^*_2\) obtained from \(C^{**}\) are isomorphic. Hence it follows that the cohomologies of the double complex are determined up to isomorphism in each dimension.

Reviewer: Vladislav A.Martynyuk (Kyïv)

MSC:

55U15	Chain complexes in algebraic topology
55N99	Homology and cohomology theories in algebraic topology

Keywords:

cohomologies; double complex