{"title":"La courbe en huit sur les sphères à pointes et le noeud de huit","authors":"Pierre Dehornoy","doi":"arxiv-2409.06532","DOIUrl":null,"url":null,"abstract":"We show that, in the unit tangent bundle of a hyperbolic orbisphere with cone\npoints of order 3, 3, 4, the lift of the shortest periodic geodesic is\nhomeomorphic to the complement of the figure-eight knot in the 3-sphere. The\nproof eventually relies on the computation of some linking numbers.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"6 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 - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06532","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 show that, in the unit tangent bundle of a hyperbolic orbisphere with cone
points of order 3, 3, 4, the lift of the shortest periodic geodesic is
homeomorphic to the complement of the figure-eight knot in the 3-sphere. The
proof eventually relies on the computation of some linking numbers.
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