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Generalized Equivariant Cohomology and Stratifications

Published online by Cambridge University Press:  20 November 2018

Peter Crooks
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4 e-mail: e-mail:
Tyler Holden
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4 e-mail: e-mail:
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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.

Research Article
Copyright © Canadian Mathematical Society 2016


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