Generalized Equivariant Cohomology and Stratifications. Issue 3 (1st September 2016)

• Record Type: Journal Article
• Authors: Crooks, Peter; Holden, Tyler
• Is Part Of: Canadian mathematical bulletin =. Volume 59:Issue 3(2016)
• Page Start: 483
• Page End: 496
• Publication Date: 2016-09-01
• Subjects: 55N91 -- 19L47; equivariant cohomology theory -- stratification -- affine Grassmannian; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2016-032-5
• Languages: English
• ISSNs: 0008-4395

Abstract

Abstract: 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.