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Geodesic complexity of a cube

Published 8 Aug 2023 in math.MG and cs.CG | (2308.04316v1)

Abstract: The topological (resp. geodesic) complexity of a topological (resp. metric) space is roughly the smallest number of continuous rules required to choose paths (resp. shortest paths) between any points of the space. We prove that the geodesic complexity of a cube exceeds its topological complexity by exactly 2. The proof involves a careful analysis of cut loci of the cube.

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