Covering complexity, scalar curvature, and quantitative $K$-theory

IF 0.5 4区数学 Q3 MATHEMATICS

Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI:10.4310/pamq.2023.v19.n6.a13

Hao Guo, Guoliang Yu

引用次数: 0

Abstract

We establish a relationship between a certain notion of covering complexity of a Riemannian spin manifold and positive lower bounds on its scalar curvature. This makes use of a pairing between quantitative operator $K$-theory and Lipschitz topological $K$-theory, combined with an earlier vanishing theorem for the quantitative higher index.

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覆盖复杂性、标量曲率和定量 $K$ 理论

我们建立了黎曼自旋流形的某种覆盖复杂性概念与其标量曲率正下限之间的关系。这利用了定量算子 $K$ 理论和 Lipschitz 拓扑 $K$ 理论之间的配对，并结合了早先的定量高指数消失定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Pure and Applied Mathematics Quarterly 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.