In some fields of studies, for example, Amenability of Banach algebras and $L^2$-Betti numbers, some chain complexes are studied, why is the study of these creatures important? When and why do these objects and their related structures enter mathematics?
closed as too broad by Anton Fetisov, LSpice, Neil Hoffman, Stefan Waldmann, Yemon Choi May 13 at 23:11
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