Equivariant $3$-manifolds with positive scalar curvature

In this paper, for any compact Lie group $G$, we show that the space of $G$-invariant Riemannian metrics with positive scalar curvature (PSC) on any closed three-manifold is either empty or contractible. In particular, we prove the generalized Smale conjecture for spherical three-orbifolds. Moreover, for connected $G$, we make a classification of all PSC $G$-invariant three-manifolds.

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