Torsion in the magnitude homology of graphs

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2021-05-15 DOI:10.1007/s40062-021-00281-9

Radmila Sazdanovic, Victor Summers

引用次数: 8

Abstract

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.

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图的大小同调中的扭转

幅度同调是heppworth和Willerton定义的有限图的一种梯度同调理论，它分类了由Leinster引入的幂级数不变量幅度。我们分析了扭量同调的结构和意义。我们证明了任何有限生成的阿贝尔群都可以作为图的幅度同调的子群出现，特别是，给定素数阶的扭转可以出现在图的幅度同调中，并且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备计算，并着重讨论了大小同调主对角线上群的秩。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.