GKM actions on cohomogeneity one manifolds

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Oliver Goertsches, University of Marburg

Online Talk

Zoom link: https://princeton.zoom.us/j/92116764865(link is external)

Passcode: 114700

Guillemin, Holm and Zara showed that a homogeneous space G/H of compact Lie groups of equal rank is a GKM manifold with respect to the action of a maximal torus of H, and determined the corresponding GKM graph in terms of the root data of G and H. In this talk we consider the analogous question for G-actions of cohomogeneity one, i.e., with an orbit of codimension 1. We find easy-to-check necessary and sufficient conditions for a maximal torus of G to act in a GKM fashion in terms of the group diagram of the action, and determine the corresponding GKM graph. We illustrate the results using the known classifications of cohomogeneity one actions with a fixed point, as well as in dimensions up to 6.

This is joint work with Eugenia Loiudice and Giovanni Russo.