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In differential geometry, the equivariant index theorem, of which there are several variants, computes the (graded) trace of an element of a compact Lie group acting in given setting in terms of the integral over the fixed points of the element. If the element is neutral, then the theorem reduces to the usual index theorem. The classical formula such as the Atiyah–Bott formula is a special case of the theorem.

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  • Äquivarianter Indexsatz (de)
  • Equivariant index theorem (en)
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  • In der Mathematik ist der äquivariante Indexsatz eine von Michael Atiyah, Graeme Segal und Isadore Singer bewiesene Formel für die von Elementen einer mit einem Dirac-Operator kommutierenden Gruppenwirkung, die die Berechnung des äquivarianten Indexes von Dirac-Operatoren aus dem -Geschlecht der Fixpunktmenge und dem äquivarianten Chern-Charakter ermöglicht. Als Spezialfall erhält man die Fixpunktformel von Atiyah–Bott. (de)
  • In differential geometry, the equivariant index theorem, of which there are several variants, computes the (graded) trace of an element of a compact Lie group acting in given setting in terms of the integral over the fixed points of the element. If the element is neutral, then the theorem reduces to the usual index theorem. The classical formula such as the Atiyah–Bott formula is a special case of the theorem. (en)
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  • In der Mathematik ist der äquivariante Indexsatz eine von Michael Atiyah, Graeme Segal und Isadore Singer bewiesene Formel für die von Elementen einer mit einem Dirac-Operator kommutierenden Gruppenwirkung, die die Berechnung des äquivarianten Indexes von Dirac-Operatoren aus dem -Geschlecht der Fixpunktmenge und dem äquivarianten Chern-Charakter ermöglicht. Als Spezialfall erhält man die Fixpunktformel von Atiyah–Bott. (de)
  • In differential geometry, the equivariant index theorem, of which there are several variants, computes the (graded) trace of an element of a compact Lie group acting in given setting in terms of the integral over the fixed points of the element. If the element is neutral, then the theorem reduces to the usual index theorem. The classical formula such as the Atiyah–Bott formula is a special case of the theorem. (en)
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