{"title":"On ends of finite-volume noncompact manifolds of nonpositive curvature","authors":"Ran Ji, Yunhui Wu","doi":"10.1007/s00222-024-01266-0","DOIUrl":null,"url":null,"abstract":"<p>In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold <span>\\(M\\)</span> of finite volume with sectional curvature <span>\\(-1 \\leq K \\leq 0\\)</span>, if the universal cover of <span>\\(M\\)</span> is a visibility manifold, then the fundamental group of each end of <span>\\(M\\)</span> is almost nilpotent.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00222-024-01266-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
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Abstract
In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold \(M\) of finite volume with sectional curvature \(-1 \leq K \leq 0\), if the universal cover of \(M\) is a visibility manifold, then the fundamental group of each end of \(M\) is almost nilpotent.
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