论文标题
大小同源性，对角，中值，库纳斯和梅耶 - 越野
Magnitude Homology, Diagonality, Medianness, Künneth and Mayer-Vietoris
论文作者
论文摘要
图形的幅度同源性由Arxiv中的Hepworth和Willerton引入：1505.04125。 Leinster和Shulman在Arxiv中的任意度量空间的幅度同源：1711.00802V2。我们验证了Arxiv中证明的Künneth和Mayer-Vietoris公式：1505.04125的图表自然扩展到公制设置。对角度的概念也是如此，也源自Arxiv：1505.04125。该概念在产品，缩回，过滤的稳定性得到验证，作为应用，表明中位空间是对角线的。特别是，任何Menger凸点的中位空间都具有消失的幅度同源性。最后，我们主张在“中间空间”的背景下对幅度同源性的定义，并发展其某些属性。
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.
