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arXiv · 1410.5740

Equivariant formality of isotropic torus actions

Jeffrey D. Carlson
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Abstract

Considering the potential equivariant formality of the left action of a connected Lie group $K$ on the homogeneous space $G/K$, we arrive through a sequence of reductions at the case $G$ is compact and simply-connected and $K$ is a torus. We then classify all pairs $(G,S)$ such that $G$ is compact connected Lie and the embedded circular subgroup $S$ acts equivariantly formally on $G/S$. In the process we provide a proof of the structure (known to Leray and Koszul) of the cohomology rings $H^*(G/S;\mathbb Q)$.

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Jeffrey D. Carlson. 2014-10-21. Equivariant formality of isotropic torus actions. https://doi.org/10.1007/s40062-018-0207-5

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