4. A chain complex C(X) is a notation to encode information about a space X. It comes as a list of abelian-, which are very simple, groups

... E_2 -> E_1 -> E_0 -> 0

connected by maps (differentials, boundary operators), one for every arrow:

d_1: E_1 -> E_0

such that applying two consecutive ones to any element yields an identity element:

d_1(d_2(e)) = id_E_0

For example: ... (read on)

#chainComplex #boundaryOperator #differential