Topological K-theory of spaces

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:logic
gptkbp:appliesTo	topological spaces
gptkbp:category	gptkb:cohomology_theory
gptkbp:field	gptkb:topology
gptkbp:generalizes	gptkb:Grothendieck_group
gptkbp:hasApplication	topological phases of matter classification of D-branes index of elliptic operators
gptkbp:hasVariant	gptkb:complex_K-theory gptkb:real_K-theory
https://www.w3.org/2000/01/rdf-schema#label	Topological K-theory of spaces
gptkbp:introduced	gptkb:Friedrich_Hirzebruch gptkb:Michael_Atiyah gptkb:Alexander_Grothendieck
gptkbp:notation	K(X) KO(X) KU(X)
gptkbp:relatedTo	gptkb:Bott_periodicity_theorem gptkb:Chern_character gptkb:Atiyah–Hirzebruch_spectral_sequence gptkb:algebraic_K-theory gptkb:twisted_K-theory equivariant K-theory
gptkbp:satisfies	Eilenberg–Steenrod axioms (except dimension axiom)
gptkbp:studies	gptkb:vector_bundles
gptkbp:usedIn	gptkb:string_theory homotopy theory index theory operator algebras
gptkbp:usedToClassify	vector bundles up to stable equivalence
gptkbp:bfsParent	gptkb:K-theory
gptkbp:bfsLayer	5