Closing curves by rearranging arcs

Leonardo Alese

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arXiv · 2002.05422

Closing curves by rearranging arcs

Leonardo Alese

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Abstract

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.

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BibTeX RIS

Leonardo Alese. 2020-02-13. Closing curves by rearranging arcs. https://arxiv.org/abs/2002.05422

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