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- KK-theory abstract "In mathematics, KK-theory is a common generalization both of K-homology and K-theory (more precisely operator K-theory), as an additive bivariant functor on separable C*-algebras. This notion was introduced by the Russian mathematician Gennadi Kasparov in 1980.It was influenced by Atiyah's concept of Fredholm modules for the Atiyah–Singer index theorem, and the classification of extensions of C*-algebras by Brown–Douglas–Fillmore (Lawrence G. Brown, Ronald G. Douglas, Peter Arthur Fillmore 1977). In turn, it has had great success in operator algebraic formalism toward the index theory and the classification of nuclear C*-algebras, as it was the key to the solutions of many problems in operator K-theory, such as, for instance, the mere calculation of K-groups. Furthermore, it was essential in the development of the Baum–Connes conjecture and plays a crucial role in noncommutative topology.KK-theory was followed by a series of similar bifunctor constructions such as the E-theory and the bivariant periodic cyclic theory, most of them having more category-theoretic flavors, or concerning another class of algebras rather than that of the separable C*-algebras, or incorporating group actions.".
- KK-theory wikiPageExternalLink books?id=wfoCkgAACAAJ.
- KK-theory wikiPageID "13314087".
- KK-theory wikiPageLength "6995".
- KK-theory wikiPageOutDegree "28".
- KK-theory wikiPageRevisionID "670756133".
- KK-theory wikiPageWikiLink Atiyah–Singer_index_theorem.
- KK-theory wikiPageWikiLink Baum–Connes_conjecture.
- KK-theory wikiPageWikiLink Bivariant_periodic_cyclic_theory.
- KK-theory wikiPageWikiLink Bott_periodicity.
- KK-theory wikiPageWikiLink Bott_periodicity_theorem.
- KK-theory wikiPageWikiLink C*-algebra.
- KK-theory wikiPageWikiLink C*-algebras.
- KK-theory wikiPageWikiLink Cap_product.
- KK-theory wikiPageWikiLink Category:K-theory.
- KK-theory wikiPageWikiLink Category_(mathematics).
- KK-theory wikiPageWikiLink Category_theory.
- KK-theory wikiPageWikiLink Cup_product.
- KK-theory wikiPageWikiLink E-theory.
- KK-theory wikiPageWikiLink Fredholm_module.
- KK-theory wikiPageWikiLink Functor.
- KK-theory wikiPageWikiLink Gennadi_Kasparov.
- KK-theory wikiPageWikiLink Group_action.
- KK-theory wikiPageWikiLink Hilbert_C*-module.
- KK-theory wikiPageWikiLink Hilbert_module.
- KK-theory wikiPageWikiLink Ideal_(ring_theory).
- KK-theory wikiPageWikiLink Joachim_Cuntz.
- KK-theory wikiPageWikiLink K-homology.
- KK-theory wikiPageWikiLink K-theory.
- KK-theory wikiPageWikiLink Mathematics.
- KK-theory wikiPageWikiLink Noncommutative_topology.
- KK-theory wikiPageWikiLink Nuclear_C*-algebra.
- KK-theory wikiPageWikiLink Operator_K-theory.
- KK-theory wikiPageWikiLink Ronald_G._Douglas.
- KK-theory wikiPageWikiLink Separable_space.
- KK-theory wikiPageWikiLink Split-exact.
- KK-theory wikiPageWikiLinkText "KK-theory".
- KK-theory hasPhotoCollection KK-theory.
- KK-theory wikiPageUsesTemplate Template:About.
- KK-theory wikiPageUsesTemplate Template:ILL.
- KK-theory wikiPageUsesTemplate Template:Nlab.
- KK-theory wikiPageUsesTemplate Template:Refbegin.
- KK-theory wikiPageUsesTemplate Template:Refend.
- KK-theory wikiPageUsesTemplate Template:Reflist.
- KK-theory subject Category:K-theory.
- KK-theory hypernym Generalization.
- KK-theory comment "In mathematics, KK-theory is a common generalization both of K-homology and K-theory (more precisely operator K-theory), as an additive bivariant functor on separable C*-algebras. This notion was introduced by the Russian mathematician Gennadi Kasparov in 1980.It was influenced by Atiyah's concept of Fredholm modules for the Atiyah–Singer index theorem, and the classification of extensions of C*-algebras by Brown–Douglas–Fillmore (Lawrence G. Brown, Ronald G.".
- KK-theory label "KK-theory".
- KK-theory sameAs KK-Theorie.
- KK-theory sameAs m.03c1gxw.
- KK-theory sameAs Q6331703.
- KK-theory sameAs Q6331703.
- KK-theory wasDerivedFrom KK-theory?oldid=670756133.
- KK-theory isPrimaryTopicOf KK-theory.