Independence of homogeneous GKM manifolds and symmetric spaces

Shintaro Kuroki; Grigory Solomadin

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arXiv · 2602.07734

Independence of homogeneous GKM manifolds and symmetric spaces

Shintaro Kuroki·Grigory Solomadin

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Abstract

Let $G/H$ be a simply connected homogeneous space of maximal rank. Then the maximal torus $T$-action on $G/H$ is a GKM manifold. We call the $T$-action $j$-independent if any $i(\leq j)$ pairwise distinct isotropy weights at a fixed point are linearly independent. Using weighted graphs, we show that the maximal independence of $G/H$ is $2$, $3$ or $n=\dim T$, and that the cases of $3$ or $n=\dim T$ correspond to some symmetric spaces of rank $>2$. As a corollary, using the results of Ayzenberg and Masuda, the lower-degree reduced homology groups (with appropriate coefficients) of the orbit space $T\backslash G/H$ vanish.

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BibTeX RIS

Shintaro Kuroki, Grigory Solomadin. 2026-02-08. Independence of homogeneous GKM manifolds and symmetric spaces. https://arxiv.org/abs/2602.07734

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