幅值同调、对角性、中值、Künneth和Mayer-Vietoris
Magnitude Homology, Diagonality, Medianness, Künneth and Mayer-Vietoris
摘要：
图的幅同调是由Hepworth和Willerton在arXiv：1505.04125中引入的。Leinster和Shulman在arXiv：1711.00802v2中对任意度量空间的幅度同调。我们验证了在arXiv：1505.04125中证明的图的Künneth和Mayer-Vietoris公式自然地扩展到度量设置。对角性的概念也是如此，同样起源于arXiv：1505.04125。这个概念下的产品，收缩，过滤的稳定性进行了验证，并作为一个应用程序，它表明，中位数空间是对角的，特别是，任何门格尔凸中位数空间有消失的幅度同调。最后，我们主张在“介数空间”的背景下定义的幅度同调，并开发它的一些性质。
英文摘要：
Magnitude homology of graphs is introduced by Hepworth and Willerton in arXiv:1505.04125 . Magnitude homology of arbitrary metric spaces by Leinster and Shulman in arXiv:1711.00802v2 . We verify that the Künneth and Mayer-Vietoris formulas proved in arXiv:1505.04125 for graphs extend naturally to the metric setting. The same is done for the notion of diagonality, also originating from arXiv:1505.04125 . Stability of this notion under products, retracts, filtrations is verified, and as an application, it is shown that median spaces are diagonal; in particular, any Menger convex median space has vanishing magnitude homology. Finally, we argue for a definition of magnitude homology in the context of "betweenness spaces" and develop some of its properties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
