Torsion in the magnitude homology of graphs
Torsion in the magnitude homology of graphs
复制标题
图的幅度同调性中的扭转
DOI：
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发表时间：
2019
影响因子：
0.5
通讯作者：
Victor Summers
中科院分区：
文献类型：
--
作者：
R. Sazdanovic;Victor Summers
幅值同调是赫普沃思和威勒顿定义的有限图的二阶同调理论，它对Leinster提出的称为幅值的幂级数不变量进行了分类。我们分析了挠率的结构和意义。我们表明，任何一个生成的阿贝尔群可能会出现作为一个子群的幅度同源的一个图，特别是，扭转一个给定的素数阶可以出现在幅度同源的一个图，有无限多个这样的图。最后，我们给出了一类外平面图的大小同调的完整计算，并着重讨论了群沿着大小同调的主对角线的秩。
Magnitude homology is a bigraded homology theory for finite graphs defined by Hepworth and Willerton, categorifying the power series invariant known as magnitude which was introduced by Leinster. We analyze the structure and implications of torsion in magnitude homology. We show that any finitely generated abelian group may appear as a subgroup of the magnitude homology of a graph, and, in particular, that torsion of a given prime order can appear in the magnitude homology of a graph and that there are infinitely many such graphs. Finally, we provide complete computations of magnitude homology of a class of outerplanar graphs and focus on the ranks of the groups along the main diagonal of magnitude homology.
关于欧几里德空间子集的渐近幅
影响因子：
0.5
作者：
Leinster T
通讯作者：
Leinster T
影响因子：
0.9
作者：
Leinster T
通讯作者：
Leinster T