{"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":56114,"journal":{"name":"Journal of Topology","volume":"16 2","pages":"679-719"},"PeriodicalIF":0.8000,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12299","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","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.
期刊介绍：
The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal.
The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.
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