What is ... Equivariant Cohomology
By L. Tu. 2013
169 citations recorded by the source corpus.
When a torus acts on a compact oriented manifold with isolated fixed points, the equivariant localization formula of Atiyah--Bott--Berline--Vergne converts the integral of an equivariantly closed form to a finite sum over the fixed points, providing a powerful tool for computing integrals on a manifold. This article seeks to give an accessible exposition of the equivariant localization formula.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f92bc518ea0e95fa89d93f53af9fb1d7aae3abdb
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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Discrete Mathematics and Combinatorics
- Thomas Lam
- Mark Shimozono
- Anne Schilling
- Jennifer Morse
- Luc Lapointe
- Geordie Williamson
- Mike Zabrocki
- Julianna Tymoczko
In Geometry and Topology
- Thomas Lam
- Mark Shimozono
- Geordie Williamson
- Anne Schilling
- Jennifer Morse
- Luc Lapointe
- Julianna Tymoczko
- Mike Zabrocki
In Mathematical Physics
- Geordie Williamson
- Thomas Lam
- Julianna Tymoczko
- Megumi Harada
- P. Fiebig
- Mark Shimozono
- M. Masuda
- T. Horiguchi
Citations in the corpus
- On the Spectrum of the Equivariant Cohomology Ring (2010, methodology): “For example, in [16] the equivariant cohomology ring H T(X; C) of an equivariantly formal space X was described in terms of the fixed points and the one-dimensional orbits, provided there are finitely many of each.”
- Poset pinball, GKM-compatible subspaces, and Hessenberg varieties (2010, methodology): “Our work develops out of GKM theory, named for the influential manuscript of Goresky-KottwitzMacPherson [11].”
- k-Schur Functions and Affine Schubert Calculus (2013, methodology): “53) the GKM condition since it is an instance (for F̃l) of a general method due to [57] of constructing equivariant cohomology for suitable spaces.”
- Hessenberg varieties and hyperplane arrangements (2016, background): “Then the restriction map (8.1) H∗T (X) →֒ H∗T (XT ) = ⊕ x∈XT H∗(BT ). is injective by condition (iii) and Goresky-Kottwitz-MacPherson ([18]) gave an explicit description of the image of the restriction map, which we shall explain.”
- Toric topology (2012, methodology): “According to [24], the equivariant cohomology of M is determined by the GKM graph associated withM .”
- Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties (2010, methodology): “On en déduit que l’algorithme de Braden-MacPherson peut être utilisé pour calculer les caractères des modules basculants pour les groupes algébriques.”
- Parity Sheaves (2009, unknown): “See for example [KL80], [GKM98] and [BJ01].”