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arXiv · 1608.01743

Cohomology of Commuting Varieties of Connected Compact Reductive Lie Groups

Henry Scher
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Abstract

We calculate the rational cohomology of the commuting variety $X_{G, n}$ consisting of $n$-tuples of commuting elements of a compact reductive group $G$. This is done by studying a map from a related variety $Y_{G, n}$, which has easily calculated cohomology. The proof studies the fibers of the map and uses the Vietoris-Begle theorem to prove that the induced map on rational cohomology is an isomorphism.

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Henry Scher. 2016-08-05. Cohomology of Commuting Varieties of Connected Compact Reductive Lie Groups. https://arxiv.org/abs/1608.01743

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