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.

翻译：拓扑（或度量）空间的拓扑（或测地线）复杂度大致是选择空间中任意两点间路径（或最短路径）所需连续规则的最小数量。我们证明立方体的测地线复杂度恰好比其拓扑复杂度高2。该证明涉及对立方体切割轨迹的细致分析。