Non-abelian tensor product and circular orderability of groups

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
Maxim Ivanov
{"title":"Non-abelian tensor product and circular orderability of groups","authors":"Maxim Ivanov","doi":"10.1016/j.topol.2024.109111","DOIUrl":null,"url":null,"abstract":"<div><div>For a group <em>G</em> we consider its tensor square <span><math><mi>G</mi><mo>⊗</mo><mi>G</mi></math></span> and exterior square <span><math><mi>G</mi><mo>∧</mo><mi>G</mi></math></span>. We prove that for a circularly orderable group <em>G</em>, under some assumptions on <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, its exterior square and tensor square are left-orderable. This yields an obstruction for a circularly orderable group <em>G</em> to have torsion. We apply these results to study circular orderability of tabulated virtual knot groups.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"358 ","pages":"Article 109111"},"PeriodicalIF":0.6000,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166864124002967","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

For a group G we consider its tensor square GG and exterior square GG. We prove that for a circularly orderable group G, under some assumptions on H1(G) and H2(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.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
非阿贝尔张量积与群的循环有序性
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。
求助全文
约1分钟内获得全文 去求助
来源期刊
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.
期刊最新文献
Editorial Board The Rudin-Kiesler pre-order and the Pixley-Roy spaces over ultrafilters The uniform convergence topology on separable subsets Relatively functionally countable subsets of products Extendability to Marczewski-Burstin countably representable ideals
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1