Equivariant 3-manifolds with positive scalar curvature

Chow, Tsz-Kiu Aaron; Li, Yangyang

doi:10.1090/tran/9181

Equivariant $3$-manifolds with positive scalar curvature
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by Tsz-Kiu Aaron Chow and Yangyang Li;

Trans. Amer. Math. Soc. 377 (2024), 5993-6020

DOI: https://doi.org/10.1090/tran/9181

Published electronically: June 13, 2024

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Abstract:

In this paper, for any compact Lie group $G$, we show that the space of $G$-equivariant 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 $G$-equivariant three-manifolds.

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