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arXiv · 2202.07700

GKM actions on cohomogeneity one manifolds

Oliver Goertsches·Eugenia Loiudice·Giovanni Russo
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Abstract

We consider compact manifolds $M$ with a cohomogeneity one action of a compact Lie group $G$ such that the orbit space $M/G$ is a closed interval. For $T$ a maximal torus of $G$, we find necessary and sufficient conditions on the group diagram of $M$ such that the $T$-action on $M$ is of GKM type, and describe its GKM graph. The general results are illustrated on explicit examples.

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Oliver Goertsches, Eugenia Loiudice, Giovanni Russo. 2022-02-15. GKM actions on cohomogeneity one manifolds. https://doi.org/10.1515/forum-2022-0061

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