{"title":"Positive scalar curvature and homology cobordism invariants","authors":"Hokuto Konno, Masaki Taniguchi","doi":"10.1112/topo.12299","DOIUrl":null,"url":null,"abstract":"<p>We give an obstruction to positive scalar curvature metrics on 4-manifolds with the homology <math>\n <semantics>\n <mrow>\n <msup>\n <mi>S</mi>\n <mn>1</mn>\n </msup>\n <mo>×</mo>\n <msup>\n <mi>S</mi>\n <mn>3</mn>\n </msup>\n </mrow>\n <annotation>$S^{1} \\times S^{3}$</annotation>\n </semantics></math> described in terms of homology cobordism invariants from Seiberg–Witten theory. The main tool of the proof is a relative Bauer–Furuta-type invariant on a periodic-end 4-manifold.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12299","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We give an obstruction to positive scalar curvature metrics on 4-manifolds with the homology described in terms of homology cobordism invariants from Seiberg–Witten theory. The main tool of the proof is a relative Bauer–Furuta-type invariant on a periodic-end 4-manifold.
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