Equivariant $3$-manifolds with positive scalar curvature

Tsz-Kiu Aaron Chow; Yangyang Li

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arXiv · 2109.12725

Equivariant $3$-manifolds with positive scalar curvature

Tsz-Kiu Aaron Chow·Yangyang Li

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Abstract

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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Tsz-Kiu Aaron Chow, Yangyang Li. 2021-09-26. Equivariant $3$-manifolds with positive scalar curvature. https://arxiv.org/abs/2109.12725

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