全等覆盖中 k 维收缩的增长

IF 2.4 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis Pub Date : 2024-06-05 DOI:10.1007/s00039-024-00686-7

Mikhail Belolipetsky, Shmuel Weinberger

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引用次数: 0

摘要

我们研究算术 n 维流形的绝对和同调 k 维系统沿全等覆盖的增长。我们的主要兴趣在于实阶 r≥2 的流形的增量。我们特别观察到，在 k=r 的某些情况下，增长函数趋向于在对数的幂函数和覆盖度的幂函数之间摇摆。这是一个新现象。我们还分别证明了小 k 和大 k 的预期多对数和常数幂边界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Growth of k-Dimensional Systoles in Congruence Coverings

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Growth of k-Dimensional Systoles in Congruence Coverings

We study growth of absolute and homological k-dimensional systoles of arithmetic n-manifolds along congruence coverings. Our main interest is in the growth of systoles of manifolds whose real rank r≥2. We observe, in particular, that in some cases for k=r the growth function tends to oscillate between a power of a logarithm and a power function of the degree of the covering. This is a new phenomenon. We also prove the expected polylogarithmic and constant power bounds for small and large k, respectively.

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来源期刊

Geometric and Functional Analysis 数学-数学

CiteScore

3.70

自引率

4.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.