Independence of homogeneous GKM manifolds and symmetric spaces
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908819885391872 |
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| author | Kuroki, Shintaro Solomadin, Grigory |
| author_facet | Kuroki, Shintaro Solomadin, Grigory |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07734 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Independence of homogeneous GKM manifolds and symmetric spaces Kuroki, Shintaro Solomadin, Grigory Geometric Topology Algebraic Topology Combinatorics Differential Geometry 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. |
| title | Independence of homogeneous GKM manifolds and symmetric spaces |
| topic | Geometric Topology Algebraic Topology Combinatorics Differential Geometry |
| url | https://arxiv.org/abs/2602.07734 |