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- Cohomology_operation abstract "In mathematics, the cohomology operation concept became central to algebraic topology, particularly homotopy theory, from the 1950s onwards, in the shape of the simple definition that if F is a functor defining a cohomology theory, then a cohomology operation should be a natural transformation from F to itself. Throughout there have been two basic points:the operations can be studied by combinatorial means; andthe effect of the operations is to yield an interesting bicommutant theory.The origin of these studies was the work of Pontryagin, Postnikov, and Norman Steenrod, who first defined the Pontryagin square, Postnikov square, and Steenrod square operations for singular cohomology, in the case of mod 2 coefficients. The combinatorial aspect there arises as a formulation of the failure of a natural diagonal map, at cochain level. The general theory of the Steenrod algebra of operations has been brought into close relation with that of the symmetric group.In the Adams spectral sequence the bicommutant aspect is implicit in the use of Ext functors, the derived functors of Hom-functors; if there is a bicommutant aspect, taken over the Steenrod algebra acting, it is only at a derived level. The convergence is to groups in stable homotopy theory, about which information is hard to come by. This connection established the deep interest of the cohomology operations for homotopy theory, and has been a research topic ever since. An extraordinary cohomology theory has its own cohomology operations, and these may exhibit a richer set on constraints.".
- Cohomology_operation wikiPageExternalLink books?id=CF3bt4oYZ2oC.
- Cohomology_operation wikiPageExternalLink books?id=FFCaPwAACAAJ.
- Cohomology_operation wikiPageID "1226719".
- Cohomology_operation wikiPageLength "3482".
- Cohomology_operation wikiPageOutDegree "33".
- Cohomology_operation wikiPageRevisionID "652869871".
- Cohomology_operation wikiPageWikiLink Adams_spectral_sequence.
- Cohomology_operation wikiPageWikiLink Algebraic_topology.
- Cohomology_operation wikiPageWikiLink Bicommutant.
- Cohomology_operation wikiPageWikiLink CW_complex.
- Cohomology_operation wikiPageWikiLink Category:Algebraic_topology.
- Cohomology_operation wikiPageWikiLink Chain_complex.
- Cohomology_operation wikiPageWikiLink Cochain.
- Cohomology_operation wikiPageWikiLink Cohomology.
- Cohomology_operation wikiPageWikiLink Cohomology_theory.
- Cohomology_operation wikiPageWikiLink Derived_functor.
- Cohomology_operation wikiPageWikiLink Dover_Publications.
- Cohomology_operation wikiPageWikiLink Eilenberg-MacLane_space.
- Cohomology_operation wikiPageWikiLink Eilenberg–MacLane_space.
- Cohomology_operation wikiPageWikiLink Ext_functor.
- Cohomology_operation wikiPageWikiLink Extraordinary_cohomology_theory.
- Cohomology_operation wikiPageWikiLink Functor.
- Cohomology_operation wikiPageWikiLink Homotopy.
- Cohomology_operation wikiPageWikiLink Homotopy_theory.
- Cohomology_operation wikiPageWikiLink Mathematics.
- Cohomology_operation wikiPageWikiLink Natural_diagonal.
- Cohomology_operation wikiPageWikiLink Natural_transformation.
- Cohomology_operation wikiPageWikiLink Norman_Steenrod.
- Cohomology_operation wikiPageWikiLink Pontryagin_cohomology_operation.
- Cohomology_operation wikiPageWikiLink Pontryagin_square.
- Cohomology_operation wikiPageWikiLink Postnikov_square.
- Cohomology_operation wikiPageWikiLink Princeton_University_Press.
- Cohomology_operation wikiPageWikiLink Representable_functor.
- Cohomology_operation wikiPageWikiLink Secondary_cohomology_operation.
- Cohomology_operation wikiPageWikiLink Singular_cohomology.
- Cohomology_operation wikiPageWikiLink Singular_homology.
- Cohomology_operation wikiPageWikiLink Stable_homotopy_theory.
- Cohomology_operation wikiPageWikiLink Steenrod_algebra.
- Cohomology_operation wikiPageWikiLink Steenrod_square.
- Cohomology_operation wikiPageWikiLink Symmetric_group.
- Cohomology_operation wikiPageWikiLink Yoneda_lemma.
- Cohomology_operation wikiPageWikiLinkText "Cohomology operation".
- Cohomology_operation wikiPageWikiLinkText "cohomology operation".
- Cohomology_operation hasPhotoCollection Cohomology_operation.
- Cohomology_operation wikiPageUsesTemplate Template:Citation.
- Cohomology_operation subject Category:Algebraic_topology.
- Cohomology_operation hypernym Functor.
- Cohomology_operation comment "In mathematics, the cohomology operation concept became central to algebraic topology, particularly homotopy theory, from the 1950s onwards, in the shape of the simple definition that if F is a functor defining a cohomology theory, then a cohomology operation should be a natural transformation from F to itself.".
- Cohomology_operation label "Cohomology operation".
- Cohomology_operation sameAs m.04k2wl.
- Cohomology_operation sameAs Q5141397.
- Cohomology_operation sameAs Q5141397.
- Cohomology_operation wasDerivedFrom Cohomology_operation?oldid=652869871.
- Cohomology_operation isPrimaryTopicOf Cohomology_operation.