Atiyah–Singer index theorem

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept
gptkbp:appliesTo	compact manifolds elliptic differential operators
gptkbp:field	gptkb:topology differential geometry mathematical analysis global analysis
gptkbp:formedBy	gptkb:Michael_Atiyah gptkb:Isadore_Singer
gptkbp:generalizes	gptkb:Gauss–Bonnet_theorem gptkb:Hirzebruch_signature_theorem gptkb:Riemann–Roch_theorem
gptkbp:hasApplication	gptkb:algebraic_geometry gptkb:quantum_field_theory gptkb:K-theory mathematical physics number theory representation theory
https://www.w3.org/2000/01/rdf-schema#label	Atiyah–Singer index theorem
gptkbp:influenced	gptkb:quantum_field_theory gptkb:string_theory noncommutative geometry
gptkbp:publishedIn	gptkb:Annals_of_Mathematics
gptkbp:relatedConcept	gptkb:Chern_character gptkb:Fredholm_operator gptkb:K-theory gptkb:Todd_class cohomology index of an operator
gptkbp:state	The analytical index of an elliptic differential operator on a compact manifold equals its topological index.
gptkbp:yearProposed	1963
gptkbp:bfsParent	gptkb:Michael_Atiyah
gptkbp:bfsLayer	4