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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 wikiPageRevisionID "482550724".
- Cohomology_operation hasPhotoCollection Cohomology_operation.
- Cohomology_operation subject Category:Algebraic_topology.
- 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=482550724.
- Cohomology_operation isPrimaryTopicOf Cohomology_operation.