Localization formula for equivariant cohomology¶
The localization theorem for equivariant cohomology in non-rational coefficients is discussed in Daniel Quillen's papers.
Core Idea¶
Localization formula for equivariant cohomology is treated here as the recurring mathematics, logic, and statistics identity summarized by this source-grounded definition: The localization theorem for equivariant cohomology in non-rational coefficients is discussed in Daniel Quillen's papers. In differential geometry, the localization formula states that for an equivariantly closed equivariant differential form \alpha on an orbifold M with a torus action and for a sufficient small \xi in the Lie algebra of the torus T, we have. {1 \over dM} \intM \alpha(\xi) = \sumF {1 \over dF} \intF {\alpha(\xi) \over eT(F)(\xi)}. where the.
Scope of Application¶
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Documented setting. The formula allows one to compute the equivariant cohomology ring of the orbifold M (a particular kind of differentiable stack) from the equivariant cohomology of its fixed point components, up to.
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History. An alternative name for the formula is Borel cohomology, after Armand Borel.
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Non-abelian localization. The localization theorem states that the equivariant cohomology can be recovered, up to torsion elements, from the equivariant cohomology of the fixed point subset.
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Non-abelian localization. But, there is still a version of the localization theorem for non-abelian actions.
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Non-abelian localization. This does not extend, in verbatim, to the non-abelian action.
Clarity¶
A clear use of Localization formula for equivariant cohomology names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The localization theorem for equivariant cohomology in non-rational coefficients is discussed in Daniel Quillen's papers.
Manages Complexity¶
Localization formula for equivariant cohomology compresses multiple mathematics, logic, and statistics details into a stable diagnostic relation. The source shows both the central mechanism—where H is Hamiltonian for the circle action, the sum is over points fixed by the circle action and \alphaj(p) are eigenvalues on the tangent space at p (cf.—and the practical consequence—this does not extend, in verbatim, to the non-abelian action.
Abstract Reasoning¶
- Type the carrier. Identify the mathematics, logic, and statistics entities to which the claim applies.
- State the relation. Use the source-grounded identity: The localization theorem for equivariant cohomology in non-rational coefficients is discussed in Daniel Quillen's papers.
- Check operation and conditions. An alternative name for the formula is Borel cohomology, after Armand Borel.
- Demand recognition evidence. The localization theorem states that the equivariant cohomology can be recovered, up to torsion elements, from the equivariant cohomology of the fixed point subset.
- Test variation.
Knowledge Transfer¶
Within the home domain. Knowledge about Localization formula for equivariant cohomology transfers literally when a new case preserves the same carrier type, relation, and recognition test. The formula allows one to compute the equivariant cohomology ring of the orbifold M (a particular kind of differentiable stack) from the equivariant cohomology of its fixed point components, up to multiplicities and Euler forms. An alternative name for the formula is Borel cohomology, after Armand Borel. Beyond the home domain. No canonical parent is asserted for Localization formula for equivariant cohomology.
Neighborhood in Abstraction Space¶
Localization formula for equivariant cohomology sits in a moderately populated region (53rd percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Algebraic Structures, Groups & Operators (42 abstractions)
Nearest neighbors
- Kirwan map — 0.88
- Classifying space for SO(n) — 0.86
- Hochschild homology — 0.86
- Deligne–Lusztig theory — 0.85
- Steenrod problem — 0.85
Computed from structural-signature embeddings · 2026-10-08