Generalized Equivariant Cohomology and Stratifications

Canadian mathematical bulletin

Tyler Holden¹  Peter Crooks¹ 

[1] Department of Mathematics, University of Toronto , Toronto, ON M5S 2E4

关键词: equivariant cohomology theory;    stratification;    affine Grassmannian;   

DOI  :  10.4153/CMB-2016-032-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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 $E_T^*(X)$ as an $E_T^*(ext{pt})$-module when $X$ is a direct limit of smooth complex projective $T_{mathbb{C}}$-varieties with finitely many $T$-fixed points and $E_T^*$ is one of $H_T^*(cdot;mathbb{Z})$, $K_T^*$, and $MU_T^*$. We perform this computation on the affineGrassmannian of a complex semisimple group.

【 授权许可】

Unknown