Emmy-Noether-Seminar: GKM actions on cohomogeneity one manifolds

GKM actions on cohomogeneity one manifolds

Eugenia Loiudice (Marburg)

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. We apply our method to numerous examples; thus we easily establish for instance which of the cohomogeneity one manifolds with a fixed point, or of dimension up to six are of GKM type. This is joint work with Oliver Goertsches and Giovanni Russo.