Boundary rigidity of CAT(0) cube complexes

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-22 DOI:10.1016/j.jctb.2024.07.003

Jérémie Chalopin, Victor Chepoi

引用次数: 0

Abstract

In this note, we prove that finite CAT(0) cube complexes can be reconstructed from their boundary distances (computed in their 1-skeleta). This result was conjectured by Haslegrave, Scott, Tamitegama, and Tan (2023). The reconstruction of a finite cell complex from the boundary distances is the discrete version of the boundary rigidity problem, which is a classical problem from Riemannian geometry. In the proof, we use the bijection between CAT(0) cube complexes and median graphs, and corner peelings of median graphs.

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CAT(0) 立方体复合物的边界刚度

在本论文中，我们证明了有限 CAT(0) 立方复数可以通过其边界距离（以其 1-skeleta 计算）来重建。这一结果是由 Haslegrave、Scott、Tamitegama 和 Tan（2023 年）猜想出来的。从边界距离重构有限单元复数是边界刚度问题的离散版本，而边界刚度问题是黎曼几何中的经典问题。在证明过程中，我们使用了 CAT(0) 立方体复数与中值图之间的双射关系，以及中值图的角剥离。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.