非阿贝尔张量积与群的循环有序性

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-10-18 DOI:10.1016/j.topol.2024.109111

引用次数: 0

摘要

对于一个群 G，我们考虑它的张量平方 G⊗G 和外部平方 G∧G。我们证明，对于一个可循环有序群 G，在 H1(G) 和 H2(G) 的一些假设下，它的外部平方和张量平方都是可左序的。这就产生了循环有序群 G 具有扭转性的障碍。我们将这些结果应用于研究表虚结群的圆有序性。

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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Non-abelian tensor product and circular orderability of groups

For a group G we consider its tensor square

G \otimes G

and exterior square

G \land G

. We prove that for a circularly orderable group G, under some assumptions on

H_{1} (G)

and

H_{2} (G)

, its exterior square and tensor square are left-orderable. This yields an obstruction for a circularly orderable group G to have torsion. We apply these results to study circular orderability of tabulated virtual knot groups.

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.