K-theory of topological spaces

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:logic
gptkbp:appliesTo	CW complexes topological spaces manifolds
gptkbp:category	gptkb:cohomology_theory
gptkbp:field	gptkb:mathematics gptkb:topology
gptkbp:generalizes	gptkb:Grothendieck_group
gptkbp:hasApplication	gptkb:C*-algebras gptkb:operator_K-theory gptkb:K-homology condensed matter physics mathematical physics noncommutative geometry topological phases of matter topological insulators elliptic operators stable homotopy theory classification of D-branes index theorem index of Fredholm operators vector bundle modification
gptkbp:hasVariant	gptkb:complex_K-theory gptkb:real_K-theory gptkb:twisted_K-theory equivariant K-theory
https://www.w3.org/2000/01/rdf-schema#label	K-theory of topological spaces
gptkbp:introduced	gptkb:Friedrich_Hirzebruch gptkb:Michael_Atiyah gptkb:Alexander_Grothendieck
gptkbp:notation	K(X) KO(X) KU(X)
gptkbp:output	abelian group
gptkbp:relatedTo	gptkb:Bott_periodicity_theorem gptkb:Chern_character gptkb:Atiyah–Hirzebruch_spectral_sequence gptkb:algebraic_K-theory gptkb:cohomology_theory homotopy theory topological K-theory vector bundle classification
gptkbp:studies	gptkb:vector_bundles
gptkbp:usedIn	gptkb:string_theory index theory operator algebras
gptkbp:bfsParent	gptkb:higher_algebraic_K-theory
gptkbp:bfsLayer	7