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Generalized Equivariant Cohomology and Stratifications

Published online by Cambridge University Press:  20 November 2018

Peter Crooks  and
Tyler Holden
Peter Crooks
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4 e-mail: peter.crooks@utoronto.ca tholden@math.toronto.edu e-mail: tholden@math.toronto.edu
Tyler Holden
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4 e-mail: peter.crooks@utoronto.ca tholden@math.toronto.edu e-mail: tholden@math.toronto.edu
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Abstract

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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.

Keywords

55N9119L47equivariant cohomology theorystratificationaffine Grassmannian

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 3 , 01 September 2016 , pp. 483 - 496
Copyright
Copyright © Canadian Mathematical Society 2016

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