CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Generalized Equivariant Cohomology and Stratifications

  Published:2016-06-22
 Printed: Sep 2016
  • Peter Crooks,
    Department of Mathematics, University of Toronto , Toronto, ON M5S 2E4
  • Tyler Holden,
    Department of Mathematics, University of Toronto , Toronto, ON M5S 2E4
Format:   LaTeX   MathJax   PDF  

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 $E_T^*(X)$ as an $E_T^*(\text{pt})$-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 affine Grassmannian of a complex semisimple group.
Keywords: equivariant cohomology theory, stratification, affine Grassmannian equivariant cohomology theory, stratification, affine Grassmannian
MSC Classifications: 55N91, 19L47 show english descriptions Equivariant homology and cohomology [See also 19L47]
Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]
55N91 - Equivariant homology and cohomology [See also 19L47]
19L47 - Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/