Equivariant 3-manifolds with positive scalar curvature

IF 1.2 2区数学 Q1 MATHEMATICS Transactions of the American Mathematical Society Pub Date : 2024-04-03 DOI:10.1090/tran/9181

Tsz-Kiu Aaron Chow, Yangyang Li

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Abstract

In this paper, for any compact Lie group G G , we show that the space of G 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 G , we make a classification of all PSC G G -equivariant three-manifolds.

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具有正标量曲率的等变 3-漫游

在本文中，对于任何紧凑的李群 G G，我们证明了在任何封闭的三芒星上具有正标量曲率（PSC）的 G G -后变黎曼度量空间要么是空的，要么是可收缩的。特别是，我们证明了球面三球面的广义斯马尔猜想。此外，对于连通的 G G，我们对所有 PSC G G - 可变三芒星进行了分类。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.

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