Generalized Equivariant Cohomology and Stratifications. Issue 3 (1st September 2016) - Crooks, Peter; Holden, Tyler
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.