Matches in DBpedia 2016-04 for { <http://wikidata.dbpedia.org/resource/Q5141397> ?p ?o }
Showing triples 1 to 32 of
32
with 100 triples per page.
- Q5141397 subject Q8800142.
- Q5141397 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.".
- Q5141397 wikiPageExternalLink books?id=CF3bt4oYZ2oC.
- Q5141397 wikiPageExternalLink books?id=FFCaPwAACAAJ.
- Q5141397 wikiPageWikiLink Q1095056.
- Q5141397 wikiPageWikiLink Q1143328.
- Q5141397 wikiPageWikiLink Q1198376.
- Q5141397 wikiPageWikiLink Q1384902.
- Q5141397 wikiPageWikiLink Q1385051.
- Q5141397 wikiPageWikiLink Q1442189.
- Q5141397 wikiPageWikiLink Q1708210.
- Q5141397 wikiPageWikiLink Q189061.
- Q5141397 wikiPageWikiLink Q212803.
- Q5141397 wikiPageWikiLink Q2137023.
- Q5141397 wikiPageWikiLink Q2901650.
- Q5141397 wikiPageWikiLink Q320245.
- Q5141397 wikiPageWikiLink Q320577.
- Q5141397 wikiPageWikiLink Q386320.
- Q5141397 wikiPageWikiLink Q395.
- Q5141397 wikiPageWikiLink Q4680481.
- Q5141397 wikiPageWikiLink Q5349490.
- Q5141397 wikiPageWikiLink Q7228372.
- Q5141397 wikiPageWikiLink Q7234407.
- Q5141397 wikiPageWikiLink Q7443815.
- Q5141397 wikiPageWikiLink Q746083.
- Q5141397 wikiPageWikiLink Q7595767.
- Q5141397 wikiPageWikiLink Q7605884.
- Q5141397 wikiPageWikiLink Q849512.
- Q5141397 wikiPageWikiLink Q864475.
- Q5141397 wikiPageWikiLink Q8800142.
- Q5141397 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.".
- Q5141397 label "Cohomology operation".