论文标题
通过重新安排弧线结束曲线
Closing curves by rearranging arcs
论文作者
论文摘要
在本文中，我们展示了如何在令人惊讶的弱假设下，将平面曲线拆分为三个弧并重新安排它们（匹配切线方向）以获得封闭曲线。我们还将这种构造概括为曲线分为$ k $弧，并通过重新安排弧线以在更高维度的曲线中来评论可以实现的目标。证明仅涉及基础拓扑的工具，而论文大多是独立的。
In this paper we show how, under surprisingly weak assumptions, one can split a planar curve into three arcs and rearrange them (matching tangent directions) to obtain a closed curve. We also generalize this construction to curves split into $k$ arcs and comment what can be achieved by rearranging arcs for a curve in higher dimensions. Proofs involve only tools from elementary topology, and the paper is mostly self-contained.
