The -Equivariant Yamabe Invariant of 3-Manifolds

Abstract

We show that the S-1-equivariant Yamabe invariant of the 3-sphere, endowed with the Hopf action, is equal to the (non-equivariant) Yamabe invariant of the 3-sphere. More generally, we establish a topological upper bound for the S-1-equivariant Yamabe invariant of any closed oriented 3-manifold endowed with an S-1-action. Furthermore, we prove a convergence result for the equivariant Yamabe constants of an accumulating sequence of subgroups of a compact Lie group acting on a closed manifold.