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GKM actions on cohomogeneity one manifolds

  • Oliver Goertsches , Eugenia Loiudice EMAIL logo and Giovanni Russo
Published/Copyright: January 30, 2023

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.

MSC 2010: 57S15; 57R91; 57S25

Communicated by Karin Melnick


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Received: 2022-02-22
Revised: 2022-11-16
Published Online: 2023-01-30
Published in Print: 2023-03-01

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