The equivariant cohomology of isotropy actions on symmetric spaces (Q418683)
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scientific article; zbMATH DE number 6039004
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The equivariant cohomology of isotropy actions on symmetric spaces |
scientific article; zbMATH DE number 6039004 |
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The equivariant cohomology of isotropy actions on symmetric spaces (English)
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29 May 2012
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Let \((G,K)\) be a Riemannian symmetric pair of the compact type such that \(G\) and \(K\) are connected Lie groups. The author shows that the \(K\)-action on the symmetric space \(G/K\) by left translation is equivariantly formal. Certain results in this direction were previously known for example in the case of \(K\) and \(G\) having equal rank and for symmetric spaces of ``type II'', that is symmetric spaces that are compact Lie groups.
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equivariant cohomology
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isotropa action
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symmetric space
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