{"title":"关于瑟斯顿的欧拉一类猜想","authors":"David Gabai, Mehdi Yazdi","doi":"10.4310/ACTA.2020.V225.N2.A3","DOIUrl":null,"url":null,"abstract":"In 1976, Thurston proved that taut foliations on closed hyperbolic 3-manifolds have Euler class of norm at most one, and conjectured that, conversely, any Euler class with norm equal to one is Euler class of a taut foliation. We construct counterexamples to this conjecture and suggest an alternative conjecture.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":null,"pages":null},"PeriodicalIF":4.9000,"publicationDate":"2016-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"On Thurston’s Euler class-one conjecture\",\"authors\":\"David Gabai, Mehdi Yazdi\",\"doi\":\"10.4310/ACTA.2020.V225.N2.A3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In 1976, Thurston proved that taut foliations on closed hyperbolic 3-manifolds have Euler class of norm at most one, and conjectured that, conversely, any Euler class with norm equal to one is Euler class of a taut foliation. We construct counterexamples to this conjecture and suggest an alternative conjecture.\",\"PeriodicalId\":50895,\"journal\":{\"name\":\"Acta Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.9000,\"publicationDate\":\"2016-03-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/ACTA.2020.V225.N2.A3\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/ACTA.2020.V225.N2.A3","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
In 1976, Thurston proved that taut foliations on closed hyperbolic 3-manifolds have Euler class of norm at most one, and conjectured that, conversely, any Euler class with norm equal to one is Euler class of a taut foliation. We construct counterexamples to this conjecture and suggest an alternative conjecture.
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