{"title":"Intersection number and some metrics on Teichmüller space","authors":"Zongliang Sun, Hui Guo","doi":"10.18910/73741","DOIUrl":null,"url":null,"abstract":"Let T (X) be the Teichmüller space of a closed surface X of genus g ≥ 2, C(X) be the space of geodesic currents on X, and L : T (X)→ C(X) be the embedding introduced by Bonahon which maps a hyperbolic metric to its corresponding Liouville current. In this paper, we compare some quantitative relations and topological behaviors between the intersection number and the Teichmüller metric, the length spectrum metric and Thurston’s asymmetric metrics on T (X), respectively.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.18910/73741","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
Let T (X) be the Teichmüller space of a closed surface X of genus g ≥ 2, C(X) be the space of geodesic currents on X, and L : T (X)→ C(X) be the embedding introduced by Bonahon which maps a hyperbolic metric to its corresponding Liouville current. In this paper, we compare some quantitative relations and topological behaviors between the intersection number and the Teichmüller metric, the length spectrum metric and Thurston’s asymmetric metrics on T (X), respectively.
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