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The $\boldsymbol{S^1}$-Equivariant Yamabe Invariant of 3-Manifolds

Ammann, Bernd ; Madani, Farid ; Pilca, Mihaela


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.

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