Geodesic
Generalized Equivariant Cohomology and Stratifications
Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 483-496

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DOI

For $T$ a compact torus and $E_{T}^{*}$ a generalized $T$ -equivariant cohomology theory, we provide a systematic framework for computing $E_{T}^{*}$ in the context of equivariantly stratified smooth complex projective varieties. This allows us to explicitly compute $H_{T}^{*}\left( X \right)$ as an $H_{T}^{*}\left( pt \right)$ -module when $X$ is a direct limit of smooth complex projective ${{T}_{\mathbb{C}}}$ -varieties. We perform this computation on the affine Grassmannian of a complex semisimple group.
DOI : 10.4153/CMB-2016-032-5
Mots-clés : 55N91, 19L47, equivariant cohomology theory, stratification, affine Grassmannian 
Crooks, Peter; Holden, Tyler. Generalized Equivariant Cohomology and Stratifications. Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 483-496. doi: 10.4153/CMB-2016-032-5
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     author = {Crooks, Peter and Holden, Tyler},
     title = {Generalized {Equivariant} {Cohomology} and {Stratifications}},
     journal = {Canadian mathematical bulletin},
     pages = {483--496},
     year = {2016},
     volume = {59},
     number = {3},
     doi = {10.4153/CMB-2016-032-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-032-5/}
}
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