{"title":"Regularity of limit sets of Anosov representations","authors":"Tengren Zhang, Andrew Zimmer","doi":"10.1112/topo.12355","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we establish necessary and sufficient conditions for the limit set of a projective Anosov representation to be a <span></span><math>\n <semantics>\n <msup>\n <mi>C</mi>\n <mi>α</mi>\n </msup>\n <annotation>$C^{\\alpha }$</annotation>\n </semantics></math>-submanifold of the real projective space for some <span></span><math>\n <semantics>\n <mrow>\n <mi>α</mi>\n <mo>∈</mo>\n <mo>(</mo>\n <mn>1</mn>\n <mo>,</mo>\n <mn>2</mn>\n <mo>)</mo>\n </mrow>\n <annotation>$\\alpha \\in (1,2)$</annotation>\n </semantics></math>. We also calculate the optimal value of <span></span><math>\n <semantics>\n <mi>α</mi>\n <annotation>$\\alpha$</annotation>\n </semantics></math> in terms of the eigenvalue data of the Anosov representation.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","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.12355","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this paper, we establish necessary and sufficient conditions for the limit set of a projective Anosov representation to be a -submanifold of the real projective space for some . We also calculate the optimal value of in terms of the eigenvalue data of the Anosov representation.
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