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In mathematics, 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. ==Example== *The inflation-restriction exact sequence ::0 → ''H'' 1(''G''/''N'', ''A''''N'') → ''H'' 1(''G'', ''A'') → ''H'' 1(''N'', ''A'')''G''/''N'' → ''H'' 2(''G''/''N'', ''A''''N'') →''H'' 2(''G'', ''A'') :in group cohomology arises as the five-term exact sequence associated to the Lyndon–Hochschild–Serre spectral sequence ::''H'' ''p''(''G''/''N'', ''H'' ''q''(''N'', ''A'')) ⇒ ''H'' ''p+q''(''G, ''A'') :where ''G'' is a profinite group, ''N'' is a closed normal subgroup, and ''A'' is a ''G''-module. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Five-term exact sequence」の詳細全文を読む スポンサード リンク
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