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Equivariant index theorem
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<p>In <a href="/facts/Differential_geometry/c04XmyLu">differential geometry</a>, the equivariant index theorem, of which there are several variants, computes the (graded) trace of an element of a compact <a href="/facts/Lie_group/a9jCQyjF">Lie group</a> acting in given setting in terms of the integral over the <a href="/facts/Fixed_point_(mathematics)/vVVddTKc">fixed points</a> of the element. If the element is neutral, then the theorem reduces to the usual <a href="/facts/Index_theorem/qwcSxamI">index theorem</a>. </p><p>The classical formula such as the <a href="/facts/Atiyah%25E2%2580%2593Bott_formula/jN0IWuB8">Atiyah–Bott formula</a> is a special case of the theorem. </p>