S^1-equivariant Yamabe invariant of 3-manifolds

TL;DR

This paper demonstrates that the S^1-equivariant Yamabe invariant of the 3-sphere with Hopf action equals its classical Yamabe invariant, and extends results to general 3-manifolds with S^1-actions, including bounds and convergence properties.

Contribution

It establishes the equality of equivariant and classical Yamabe invariants for the 3-sphere and provides topological bounds and convergence results for S^1-equivariant Yamabe invariants on 3-manifolds.

Findings

S^1-equivariant Yamabe invariant of the 3-sphere equals its classical invariant

Topological upper bounds for equivariant Yamabe invariants of 3-manifolds

Convergence results for equivariant Yamabe constants of subgroup sequences

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.