2020/02/13 by Alese, Leonardo
#53A04 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2002.05422
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.