{"title":"Ribbon cobordisms as a partial order","authors":"Marius Huber","doi":"10.4310/mrl.2023.v30.n5.a8","DOIUrl":null,"url":null,"abstract":"We show that the notion of ribbon rational homology cobordism yields a partial order on the set of aspherical 3‑manifolds, thus supporting a conjecture formulated by Daemi, Lidman, Vela–Vick and Wong. Our proof is built on Agol’s recent proof of the fact that ribbon concordance yields a partial order on the set of knots in the 3‑sphere.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Research Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/mrl.2023.v30.n5.a8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We show that the notion of ribbon rational homology cobordism yields a partial order on the set of aspherical 3‑manifolds, thus supporting a conjecture formulated by Daemi, Lidman, Vela–Vick and Wong. Our proof is built on Agol’s recent proof of the fact that ribbon concordance yields a partial order on the set of knots in the 3‑sphere.
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