The S1-equivariant Yamabe invariant of 3-manifolds
by
Bernd Ammann, Farid Madani, Mihaela Pilca

The S1-equivariant Yamabe invariant of 3-manifolds (.pdf)
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Int. Math. Res. Not. (IMRN), 2017 (20), 6310-6328 (2017), doi: 10.1093/imrn/rnw194

Abstract

We show that the S1-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 S1-equivariant Yamabe invariant of any closed oriented 3-manifold endowed with an S1-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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The Paper was written on 11.8.2015
Last update 11.8.2015