Differential complex

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Definition

Given data

Let M be a differential manifold and E_is be smooth vector bundles over M. For a vector bundle E, let \Gamma(E) dneote the shead of smooth sections of E.

Definition part

A differential complex is a sequence of maps P_i: \Gamma(E_i)\to \Gamma(E_{i+1}) such that P_i \circ P_{i-1} = 0.