Compact symplectic manifolds of low cohomogeneity

Abstract

In this note we describe the equivariant diffeomorphism types of compact symplectic manifolds M which admit a Hamiltonian action of a connected compact Lie group G such that the quotient space M/ G has dimension 1. For a class of these manifolds we compute their small quantum cohomology algebra. We also construct some symplectic manifolds of cohomogeneity 2.