In differential geometry, the localization formula states that for an equivariantly closed equivariant differential form α {\displaystyle \alpha } on an...

In mathematics, equivariant cohomology (or Borel cohomology) is a cohomology theory from algebraic topology which applies to topological spaces with a...

{\sin((2\lambda +1)X)}{\sin X/2}}} Weyl character formula Localization formula for equivariant cohomology Kirillov, A. A., Lectures on the Orbit Method,...

showed how to deduce the Duistermaat–Heckman formula from a localization theorem for equivariant cohomology. Berline, Nicole; Vergne, Michele (1982), "Classes...

d_{\mathfrak {g}},} which is called the equivariant cohomology of M (which coincides with the ordinary equivariant cohomology defined in terms of Borel construction...

be deduced from a more general formula in equivariant cohomology, which was a consequence of well-known localization theorems. Atiyah showed that the...

proved equivariant analogs of fundamental theorems such as the localization theorem. Bott periodicity KK-theory KR-theory List of cohomology theories...

in terms of a localized Chern class. Over the complex numbers, the theorem is (or can be interpreted as) a special case of the equivariant index theorem...

subcomplexes. When the variety is smooth, the Chow groups can be interpreted as cohomology groups (compare Poincaré duality) and have a multiplication called the...

Kottwitz, Robert; MacPherson, Robert (1998), "Equivariant cohomology, Koszul duality, and the localization theorem", Inventiones Mathematicae, 131: 25–83...

generalized cohomology theory. Eilenberg–Zilber theorem elliptic elliptic cohomology. En-algebra equivariant algebraic topology Equivariant algebraic topoloy...

trace formula Behrend's trace formula generalizes Grothendieck's trace formula; both formulas compute the trace of the Frobenius on l-adic cohomology. big...

inner product for which the longest root has norm 2. This matches the loop algebra convention, where levels are discretized by third cohomology of simply...

frame bundle is useful because tensor fields on M can be regarded as equivariant vector-valued functions on F(M). On a manifold that is sufficiently smooth...