{"title":"解析网和拓扑网","authors":"Kirill Lazebnik","doi":"10.1016/j.aim.2024.110042","DOIUrl":null,"url":null,"abstract":"<div><div>We characterize which planar graphs arise as the pullback, under a rational map <em>r</em>, of an analytic Jordan curve passing through the critical values of <em>r</em>. We also prove that such pullbacks are dense within the collection of <span><math><msup><mrow><mi>f</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>Σ</mi><mo>)</mo></math></span>, where <em>f</em> is a branched cover of the sphere and Σ is a Jordan curve passing through the branched values of <em>f</em>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"461 ","pages":"Article 110042"},"PeriodicalIF":1.5000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytic and topological nets\",\"authors\":\"Kirill Lazebnik\",\"doi\":\"10.1016/j.aim.2024.110042\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We characterize which planar graphs arise as the pullback, under a rational map <em>r</em>, of an analytic Jordan curve passing through the critical values of <em>r</em>. We also prove that such pullbacks are dense within the collection of <span><math><msup><mrow><mi>f</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>Σ</mi><mo>)</mo></math></span>, where <em>f</em> is a branched cover of the sphere and Σ is a Jordan curve passing through the branched values of <em>f</em>.</div></div>\",\"PeriodicalId\":50860,\"journal\":{\"name\":\"Advances in Mathematics\",\"volume\":\"461 \",\"pages\":\"Article 110042\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2025-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0001870824005589\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/12/9 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870824005589","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/12/9 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We characterize which planar graphs arise as the pullback, under a rational map r, of an analytic Jordan curve passing through the critical values of r. We also prove that such pullbacks are dense within the collection of , where f is a branched cover of the sphere and Σ is a Jordan curve passing through the branched values of f.
期刊介绍：
Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.
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