Equivariant $3$-manifolds with positive scalar curvature

Tsz-Kiu Aaron Chow; Yangyang Li

Equivariant $3$-manifolds with positive scalar curvature

Differential Geometry 2022-04-21 v2 Geometric Topology

Authors: Tsz-Kiu Aaron Chow , Yangyang Li

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.

Keywords

positive scalar curvature equivariant 3-manifolds G-invariant Riemannian metrics Smale conjecture spherical 3-orbifolds compact Lie group

Cite

@article{arxiv.2109.12725,
  title  = {Equivariant $3$-manifolds with positive scalar curvature},
  author = {Tsz-Kiu Aaron Chow and Yangyang Li},
  journal= {arXiv preprint arXiv:2109.12725},
  year   = {2022}
}

Comments

22 pages, improved exposition

Related papers

View all related →