equivariant index theorem

E391908

generalization of the Atiyah–Singer index theorem index theorem mathematical theorem

The equivariant index theorem is a generalization of the Atiyah–Singer index theorem that computes indices of elliptic operators while taking into account the action of a symmetry group.

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All labels observed (2)

Label	Occurrences
Atiyah–Segal–Singer equivariant index theorem	1
equivariant index theorem canonical	1

Statements (48)

Predicate	Object
instanceOf	generalization of the Atiyah–Singer index theorem ⓘ index theorem ⓘ mathematical theorem ⓘ
appliesTo	compact Lie group actions ⓘ manifolds with group actions ⓘ
associatedWith	Graeme Segal ⓘ Isadore Singer ⓘ Michael Atiyah ⓘ
assumes	ellipticity of the operator ⓘ proper group action ⓘ
characterizes	index as an element of the representation ring ⓘ
computes	equivariant index of an elliptic operator ⓘ virtual character of a group representation ⓘ
concerns	invariance of index under equivariant deformations ⓘ localization at fixed points of the group action ⓘ
dealsWith	elliptic differential operators ⓘ equivariant K-theory ⓘ equivariant elliptic operators ⓘ fixed point formulas ⓘ group actions ⓘ
domain	compact smooth manifolds ⓘ elliptic complexes with group action ⓘ
field	differential geometry ⓘ global analysis ⓘ representation theory ⓘ topology ⓘ
generalizes	Atiyah–Singer index theorem ⓘ
hasApplicationIn	geometry of group actions ⓘ mathematical physics ⓘ representation theory of compact Lie groups ⓘ symplectic geometry ⓘ
hasVersion	equivariant index theorem self-linksurface differs ⓘ surface form: Atiyah–Segal–Singer equivariant index theorem Lefschetz fixed-point theorem ⓘ surface form: Lefschetz fixed point formula
implies	character formulas for group representations ⓘ fixed point formulas for group actions ⓘ
motivation	study of symmetry in elliptic operator theory ⓘ
output	class in the representation ring of the group ⓘ
relatedTo	Atiyah–Bott fixed-point theorem ⓘ surface form: Atiyah–Bott fixed point formula Lefschetz fixed-point theorem ⓘ surface form: Lefschetz fixed point theorem Riemann–Roch theorem ⓘ equivariant Riemann–Roch theorem ⓘ
relates	analytic index ⓘ topological index ⓘ
usesConcept	Chern character ⓘ K-theory ⓘ Todd class ⓘ K-theory ⓘ surface form: equivariant K-theory equivariant cohomology ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Atiyah–Singer index theorem → hasVariant → equivariant index theorem ⓘ

equivariant index theorem → hasVersion → equivariant index theorem self-linksurface differs ⓘ

this entity surface form: Atiyah–Segal–Singer equivariant index theorem