GKM actions on cohomogeneity one manifolds

Abstract

Abstract We consider compact manifolds M with a cohomogeneity one action of a compact Lie group G such that the orbit space M / G {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.