Topology of horocycles on geometrically finite nonpositively curved surfaces

Pub Date : 2024-07-28 DOI:10.1007/s10711-024-00941-z
Sergi Burniol Clotet
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Abstract

We study the closure of horocycles on rank 1 nonpositively curved surfaces with finitely generated fundamental group. Each horocycle is closed or dense on a certain subset of the unit tangent bundle. In fact, we classify each half-horocycle in terms of the associated geodesic rays. We also determine the nonwandering set of the horocyclic flow and characterize the surfaces admitting a minimal set for this flow.

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几何有限非正曲面上的角环拓扑学
我们研究具有有限生成基群的 1 级非正曲曲面上的角循环闭合。每个角循环都在单位切线束的某个子集上封闭或密集。事实上,我们根据相关的大地射线对每个半角环进行了分类。我们还确定了角环流的非漫游集,并描述了容纳该流最小集的曲面的特征。
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