{"title":"Nonabelianness of fundamental group of flat spacetime","authors":"Gunjan Agrawal, Deepanshi","doi":"10.1016/S0034-4877(24)00036-3","DOIUrl":null,"url":null,"abstract":"<div><p>In the present paper, it has been obtained that the fundamental group of <em>n</em>-dimensional Minkowski space with the time topology contains uncountably many copies of the additive group of integers and is not abelian. The result has been first proved for <em>n</em> = 2. Thereafter, it is extended to <em>n</em> > 2 by proving that loops nonhomotopic in <em>M</em><sup>2</sup> continue to be nonhomotopic in <em>M<sup>n</sup></em> using embedding of <em>M</em><sup>2</sup> in <em>M<sup>n</sup></em> as a retract through the projection map.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000363","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In the present paper, it has been obtained that the fundamental group of n-dimensional Minkowski space with the time topology contains uncountably many copies of the additive group of integers and is not abelian. The result has been first proved for n = 2. Thereafter, it is extended to n > 2 by proving that loops nonhomotopic in M2 continue to be nonhomotopic in Mn using embedding of M2 in Mn as a retract through the projection map.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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