Transformation Groups

, Volume 13, Issue 3–4, pp 585–615 | Cite as

Torsion and Abelianization in Equivariant Cohomology

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Abstract

Let X be a topological space upon which a compact connected Lie group G acts. It is well known that the equivariant cohomology H * G (X; Q) is isomorphic to the subalgebra of Weyl group invariants of the equivariant cohomology H * T (X; Q), where T is a maximal torus of G. This relationship breaks down for coefficient rings k other than Q. Instead, we prove that under a mild condition on k the algebra H * G (X; k) is isomorphic to the subalgebra of H * T (X; k) annihilated by the divided difference operators.

Keywords

Weyl Group Maximal Torus Zero Divisor Equivariant Cohomology Schubert Polynomial 
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Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  1. 1.Department of MathematicsCornell UniversityIthacaUSA

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