Five-term exact sequence

Five-term exact sequence

The five-term exact sequence or exact sequence of low-degree terms is a sequence of terms related to the first step of a spectral sequence.

More precisely, let:"E"2"p","q" ⇒ "H""n"("A")be a spectral sequence, whose terms are non-trivial only for "p", "q" ≥ 0.

Then there is an exact sequence:0 → "E"21,0 → "H"1("A") → "E"20,1 → "E"22,0 → "H"2("A").

Here, the map "E"20,1 → "E"22,0 is the differential of the "E"2-term of the spectral sequence.

Reference

* | year=1994


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