Equivariant 3-manifolds with positive scalar curvature

Tsz Kiu Aaron Chow; Yangyang Li

doi:10.1090/tran/9181

Equivariant 3-manifolds with positive scalar curvature

Research output: Contribution to journal › Journal Article › peer-review

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 threemanifolds.

Original language	English
Pages (from-to)	5993-6020
Number of pages	28
Journal	Transactions of the American Mathematical Society
Volume	377
Issue number	8
Early online date	13 Jun 2024
DOIs	https://doi.org/10.1090/tran/9181
Publication status	Published - Aug 2024
Externally published	Yes

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Publisher Copyright:
© 2024 by the authors.

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10.1090/tran/9181

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title = "Equivariant 3-manifolds with positive scalar curvature",

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 threemanifolds.",

author = "Chow, \{Tsz Kiu Aaron\} and Yangyang Li",

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doi = "10.1090/tran/9181",

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AU - Chow, Tsz Kiu Aaron

AU - Li, Yangyang

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N2 - 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 threemanifolds.

AB - 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 threemanifolds.

UR - https://www.scopus.com/pages/publications/85198724712

U2 - 10.1090/tran/9181

DO - 10.1090/tran/9181

M3 - Journal Article

AN - SCOPUS:85198724712

SN - 0002-9947

VL - 377

SP - 5993

EP - 6020

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 8

ER -

Equivariant 3-manifolds with positive scalar curvature

Abstract

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