CAT(0) 立方体复合物的边界刚度

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2024-07-22 DOI:10.1016/j.jctb.2024.07.003

Jérémie Chalopin, Victor Chepoi

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引用次数: 0

摘要

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。

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Boundary rigidity of CAT(0) cube complexes

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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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.