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This is a list of some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra. For other sorts of homology theories see the links at the end of this article. ==Notation== *''S'' = π = ''S''''0'' is the sphere spectrum. *''S''''n'' is the spectrum of the ''n''-dimensional sphere *''S''''n''''Y'' = ''S''''n''∧''Y'' is the ''n''th suspension of a spectrum ''Y''. *() is the abelian group of morphisms from the spectrum ''X'' to the spectrum ''Y'', given (roughly) as homotopy classes of maps. *()''n'' = () *()'' *'' is the graded abelian group given as the sum of the groups ()''n''. *π''n''(''X'') = (''X'' ) = ()''n'' is the ''n''th stable homotopy group of ''X''. *π'' *''(''X'') is the sum of the groups π''n''(''X''), and is called the coefficient ring of ''X'' when ''X'' is a ring spectrum. *''X''∧''Y'' is the smash product of two spectra. If ''X'' is a spectrum, then it defines generalized homology and cohomology theories on the category of spectra as follows. *''X''''n''(''Y'') = (''X''∧''Y'' )''n'' = (''X''∧''Y'' ) is the generalized homology of ''Y'', *''X''''n''(''Y'') = (''X'' )−''n'' = (''X'' ) is the generalized cohomology of ''Y'' 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「List of cohomology theories」の詳細全文を読む スポンサード リンク
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