Jonas BeyrerUNISTRA, Olivier GuichardUNISTRA, François LabourieUniCA, Beatrice Pozzetti, Anna Wienhard
{"title":"Positivity, cross-ratios and the Collar Lemma","authors":"Jonas BeyrerUNISTRA, Olivier GuichardUNISTRA, François LabourieUniCA, Beatrice Pozzetti, Anna Wienhard","doi":"arxiv-2409.06294","DOIUrl":null,"url":null,"abstract":"We prove that $\\Theta$-positive representations of fundamental groups of\nsurfaces (possibly cusped or of infinite type) satisfy a collar lemma, and\ntheir associated cross-ratios are positive. As a consequence we deduce that\n$\\Theta$-positive representations form closed subsets of the representation\nvariety.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06294","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 prove that $\Theta$-positive representations of fundamental groups of
surfaces (possibly cusped or of infinite type) satisfy a collar lemma, and
their associated cross-ratios are positive. As a consequence we deduce that
$\Theta$-positive representations form closed subsets of the representation
variety.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
