# The S^{1}-equivariant Yamabe invariant of 3-manifolds

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Bernd Ammann, Farid Madani, Mihaela Pilca

**The S**^{1}-equivariant Yamabe invariant of 3-manifolds
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*Int. Math. Res. Not. (IMRN)*, **2017** (20), *6310-6328* (2017), **doi: 10.1093/imrn/rnw194**

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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The Paper was written on 11.8.2015

Last update 11.8.2015