{"title":"PRESCRIBED VIRTUAL HOMOLOGICAL TORSION OF 3-MANIFOLDS","authors":"Michelle Chu, Daniel Groves","doi":"10.1017/s1474748022000329","DOIUrl":null,"url":null,"abstract":"<p>Let <span>M</span> be an irreducible <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231011174340993-0672:S1474748022000329:S1474748022000329_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$3$</span></span></img></span></span>-manifold <span>M</span> with empty or toroidal boundary which has at least one hyperbolic piece in its geometric decomposition, and let <span>A</span> be a finite abelian group. Generalizing work of Sun [20] and of Friedl–Herrmann [7], we prove that there exists a finite cover <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231011174340993-0672:S1474748022000329:S1474748022000329_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$M' \\to M$</span></span></img></span></span> so that <span>A</span> is a direct factor in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231011174340993-0672:S1474748022000329:S1474748022000329_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$H_1(M',{\\mathbb Z})$</span></span></img></span></span>.</p>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"1399 ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Institute of Mathematics of Jussieu","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s1474748022000329","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Let M be an irreducible $3$-manifold M with empty or toroidal boundary which has at least one hyperbolic piece in its geometric decomposition, and let A be a finite abelian group. Generalizing work of Sun [20] and of Friedl–Herrmann [7], we prove that there exists a finite cover $M' \to M$ so that A is a direct factor in $H_1(M',{\mathbb Z})$.
期刊介绍:
The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.