|
In algebraic topology, a transgression map is a way to transfer cohomology classes. It occurs, for example in the inflation-restriction exact sequence in group cohomology, and in integration in fibers. It also naturally arises in many spectral sequences; see spectral sequence#Edge maps and transgressions. == Inflation-restriction exact sequence == (詳細はinflation-restriction exact sequence, an exact sequence occurring in group cohomology. Let ''G'' be a group, ''N'' a normal subgroup, and ''A'' an abelian group which is equipped with an action of ''G'', i.e., a homomorphism from ''G'' to the automorphism group of ''A''. The quotient group ''G/N'' acts on ''AN = ''. Then the inflation-restriction exact sequence is: ::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'') : The transgression map is the map ''H'' 1(''N'', ''A'')''G''/''N'' → ''H'' 2(''G''/''N'', ''A''''N'') Transgression is defined for general ''n'' :''H''''n''(''N'', ''A'')''G''/''N'' → ''H''''n''+1(''G''/''N'', ''A''''N'') only if ''H''''i''(''N'', ''A'')''G''/''N'' = 0 for ''i'' ≤ ''n''-1.〔Gille & Szamuely (2006) p.67〕 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「transgression map」の詳細全文を読む スポンサード リンク
|