{"title":"On stable commutator length of non-filling curves in surfaces","authors":"Max Forester, Justin Malestein","doi":"10.1017/prm.2023.121","DOIUrl":null,"url":null,"abstract":"<p>We give a new proof of rationality of stable commutator length (scl) of certain elements in surface groups: those represented by curves that do not fill the surface. Such elements always admit extremal surfaces for scl. These results also hold more generally for non-filling <span><span><span data-mathjax-type=\"texmath\"><span>$1$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231213131917887-0965:S030821052300121X:S030821052300121X_inline1.png\"/></span></span>–chains.</p>","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"287 1 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/prm.2023.121","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We give a new proof of rationality of stable commutator length (scl) of certain elements in surface groups: those represented by curves that do not fill the surface. Such elements always admit extremal surfaces for scl. These results also hold more generally for non-filling $1$–chains.
期刊介绍：
A flagship publication of The Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics journal publishing peer-reviewed papers of international standard across the whole spectrum of mathematics, but with the emphasis on applied analysis and differential equations.
An international journal, publishing six issues per year, Proceedings A has been publishing the highest-quality mathematical research since 1884. Recent issues have included a wealth of key contributors and considered research papers.
–chains.
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