(Quasi-)Hamiltonian manifolds of cohomogeneity one

TL;DR

This paper classifies compact cohomogeneity one Hamiltonian and quasi-Hamiltonian manifolds, providing new examples and concretizing the classification of rank one multiplicity free manifolds.

Contribution

It offers a complete classification of rank one multiplicity free Hamiltonian and quasi-Hamiltonian manifolds, including new explicit examples.

Findings

Classified all such manifolds for compact, connected Lie groups.

Produced numerous new concrete examples.

Connected the classification to Hamiltonian loop group actions.

Abstract

We classify compact, connected Hamiltonian and quasi-Hamiltonian manifolds of cohomogeneity one (which is the same as being multiplicity free of rank one). Here the group acting is a compact connected Lie group (simply connected in the quasi-Hamiltonian case). This work is a concretization of the more general classification (arXiv:1612.03843) of multiplicity free manifolds in the special case of rank one. As a result we obtain numerous new concrete examples of multiplicity free quasi-Hamiltonian manifolds or, equivalently, Hamiltonian loop group actions.