Coboundary expansion is a high dimensional generalization of the Cheeger constant to simplicial complexes. Originally, this notion was motivated by the fact that it implies topological expansion, but nowadays a significant part of the motivation stems from its deep connection to problems in theoretical computer science such as agreement expansion in the low soundness regime. In this paper, we prove coboundary expansion with non-Abelian coefficients for the coset complex construction of Kaufman and Oppenheim. Our proof uses a novel global argument, as opposed to the local-to-global arguments that are used to prove cosystolic expansion.

翻译：上边缘展开是Cheeger常数向单纯复形的高维推广。最初，这一概念的提出源于其蕴含拓扑展开的性质，但如今其重要动机很大程度上源于其与理论计算机科学中诸多问题（如低可靠性区域中的一致性展开）的深刻联系。本文针对Kaufman和Oppenheim提出的余集复形构造，证明了具有非阿贝尔系数的上边缘展开性质。与证明余上循环展开时采用的局部到全局论证方法不同，我们的证明运用了一种新颖的全局论证框架。