Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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O. Goertsches - E. Loiudice - G. Russo

GKM actions on cohomogeneity one manifolds

created by russo on 16 Jan 2023
modified on 05 Apr 2023


Published Paper

Inserted: 16 jan 2023
Last Updated: 5 apr 2023

Journal: Forum Mathematicum
Volume: 35
Number: 2
Pages: 391-407
Year: 2023
Doi: 10.1515/forum-2022-0061

ArXiv: 2202.07700 PDF


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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