尖球面上的八字形曲线和八字形结

arXiv - MATH - Geometric Topology Pub Date : 2024-09-10 DOI:arxiv-2409.06532

Pierre Dehornoy

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摘要

我们证明，在具有 3、3、4 阶圆锥点的双曲球面的单位切线束中，最短周期性大地线的提升与 3 球面中的八字结的补集同构。这个证明最终依赖于一些连接数的计算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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La courbe en huit sur les sphères à pointes et le noeud de huit

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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arXiv - MATH - Geometric Topology

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