Definition
If E0, E1, ..., Ek are vector bundles on a smooth manifold M (usually taken to be compact), then a differential complex is a sequence
of differential operators between the sheaves of sections of the Ei such that Pi+1 o Pi=0. A differential complex is elliptic if the sequence of symbols
is exact outside of the zero section. Here π is the projection of the cotangent bundle T*M to M, and π* is the pullback of a vector bundle.
Read more about this topic: Elliptic Complex
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