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- Bott_periodicity_theorem abstract "In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by Raoul Bott (1957, 1959), which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres. Bott periodicity can be formulated in numerous ways, with the periodicity in question always appearing as a period-2 phenomenon, with respect to dimension, for the theory associated to the unitary group. See for example topological K-theory.There are corresponding period-8 phenomena for the matching theories, (real) KO-theory and (quaternionic) KSp-theory, associated to the real orthogonal group and the quaternionic symplectic group, respectively. The J-homomorphism is a homomorphism from the homotopy groups of orthogonal groups to stable homotopy groups of spheres, which causes the period 8 Bott periodicity to be visible in the stable homotopy groups of spheres.".
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- Bott_periodicity_theorem wikiPageWikiLink Adams_conjecture.
- Bott_periodicity_theorem wikiPageWikiLink Adjoint_functors.
- Bott_periodicity_theorem wikiPageWikiLink Algebraic_topology.
- Bott_periodicity_theorem wikiPageWikiLink Annals_of_Mathematics.
- Bott_periodicity_theorem wikiPageWikiLink Category:Homotopy_theory.
- Bott_periodicity_theorem wikiPageWikiLink Category:Theorems_in_topology.
- Bott_periodicity_theorem wikiPageWikiLink Category:Topology_of_Lie_groups.
- Bott_periodicity_theorem wikiPageWikiLink Characteristic_class.
- Bott_periodicity_theorem wikiPageWikiLink Circle.
- Bott_periodicity_theorem wikiPageWikiLink Classical_group.
- Bott_periodicity_theorem wikiPageWikiLink Classical_groups.
- Bott_periodicity_theorem wikiPageWikiLink Classification_of_Clifford_algebras.
- Bott_periodicity_theorem wikiPageWikiLink Classifying_space.
- Bott_periodicity_theorem wikiPageWikiLink Clifford_algebra.
- Bott_periodicity_theorem wikiPageWikiLink Cohomology.
- Bott_periodicity_theorem wikiPageWikiLink Daniel_Quillen.
- Bott_periodicity_theorem wikiPageWikiLink Direct_limit.
- Bott_periodicity_theorem wikiPageWikiLink George_W._Whitehead.
- Bott_periodicity_theorem wikiPageWikiLink Grassmannian.
- Bott_periodicity_theorem wikiPageWikiLink Homology_(mathematics).
- Bott_periodicity_theorem wikiPageWikiLink Homology_theory.
- Bott_periodicity_theorem wikiPageWikiLink Homotopy.
- Bott_periodicity_theorem wikiPageWikiLink Homotopy_equivalence.
- Bott_periodicity_theorem wikiPageWikiLink Homotopy_group.
- Bott_periodicity_theorem wikiPageWikiLink Homotopy_groups_of_spheres.
- Bott_periodicity_theorem wikiPageWikiLink J-homomorphism.
- Bott_periodicity_theorem wikiPageWikiLink K-theory.
- Bott_periodicity_theorem wikiPageWikiLink KO-theory.
- Bott_periodicity_theorem wikiPageWikiLink KSp-theory.
- Bott_periodicity_theorem wikiPageWikiLink Lagrangian_Grassmannian.
- Bott_periodicity_theorem wikiPageWikiLink Left_adjoint.
- Bott_periodicity_theorem wikiPageWikiLink Loop_space.
- Bott_periodicity_theorem wikiPageWikiLink Mathematics.
- Bott_periodicity_theorem wikiPageWikiLink Morse_theory.
- Bott_periodicity_theorem wikiPageWikiLink Orthogonal_group.
- Bott_periodicity_theorem wikiPageWikiLink Principal_homogeneous_space.
- Bott_periodicity_theorem wikiPageWikiLink Proceedings_of_the_National_Academy_of_Sciences.
- Bott_periodicity_theorem wikiPageWikiLink Proceedings_of_the_National_Academy_of_Sciences_of_the_United_States_of_America.
- Bott_periodicity_theorem wikiPageWikiLink Raoul_Bott.
- Bott_periodicity_theorem wikiPageWikiLink Right_adjoint.
- Bott_periodicity_theorem wikiPageWikiLink Smash_product.
- Bott_periodicity_theorem wikiPageWikiLink Sphere.
- Bott_periodicity_theorem wikiPageWikiLink Stable_homotopy_groups_of_spheres.
- Bott_periodicity_theorem wikiPageWikiLink Stable_homotopy_theory.
- Bott_periodicity_theorem wikiPageWikiLink Stiefel_manifold.
- Bott_periodicity_theorem wikiPageWikiLink Suspension_(mathematics).
- Bott_periodicity_theorem wikiPageWikiLink Suspension_(topology).
- Bott_periodicity_theorem wikiPageWikiLink Symmetric_space.
- Bott_periodicity_theorem wikiPageWikiLink Symplectic_group.
- Bott_periodicity_theorem wikiPageWikiLink Topological_K-theory.
- Bott_periodicity_theorem wikiPageWikiLink Unitary_group.
- Bott_periodicity_theorem wikiPageWikiLink Vector_bundle.
- Bott_periodicity_theorem wikiPageWikiLinkText "Bott periodicity theorem".
- Bott_periodicity_theorem wikiPageWikiLinkText "Bott periodicity".
- Bott_periodicity_theorem wikiPageWikiLinkText "Clifford algebra clock".
- Bott_periodicity_theorem wikiPageWikiLinkText "Periodicity Theorem".
- Bott_periodicity_theorem wikiPageWikiLinkText "geometric model of loop spaces".
- Bott_periodicity_theorem wikiPageWikiLinkText "geometric proof of the Bott periodicity theorem".
- Bott_periodicity_theorem wikiPageWikiLinkText "periodicity theorem".
- Bott_periodicity_theorem wikiPageWikiLinkText "periodicity".
- Bott_periodicity_theorem authorlink "Raoul Bott".
- Bott_periodicity_theorem first "Raoul".
- Bott_periodicity_theorem hasPhotoCollection Bott_periodicity_theorem.
- Bott_periodicity_theorem last "Bott".
- Bott_periodicity_theorem wikiPageUsesTemplate Template:Citation.
- Bott_periodicity_theorem wikiPageUsesTemplate Template:Harv.
- Bott_periodicity_theorem wikiPageUsesTemplate Template:Harvs.
- Bott_periodicity_theorem wikiPageUsesTemplate Template:Harvtxt.
- Bott_periodicity_theorem wikiPageUsesTemplate Template:Reflist.
- Bott_periodicity_theorem year "1957".
- Bott_periodicity_theorem year "1959".
- Bott_periodicity_theorem subject Category:Homotopy_theory.
- Bott_periodicity_theorem subject Category:Theorems_in_topology.
- Bott_periodicity_theorem subject Category:Topology_of_Lie_groups.
- Bott_periodicity_theorem type Mapping.
- Bott_periodicity_theorem type Theorem.
- Bott_periodicity_theorem comment "In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by Raoul Bott (1957, 1959), which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres.".
- Bott_periodicity_theorem label "Bott periodicity theorem".
- Bott_periodicity_theorem sameAs m.03by6k.
- Bott_periodicity_theorem sameAs Q4948983.
- Bott_periodicity_theorem sameAs Q4948983.
- Bott_periodicity_theorem sameAs 博特周期性定理.
- Bott_periodicity_theorem wasDerivedFrom Bott_periodicity_theorem?oldid=621220636.
- Bott_periodicity_theorem isPrimaryTopicOf Bott_periodicity_theorem.