Geodesic complexity of a cube

2023/08/08 by Davis, Donald M. · 1 citation
#52B10 #53C22 #55M30 #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2308.04316

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.

Cited by

• Geodesic complexity of the octahedron, and an algorithm for cut loci on convex polyhedra

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• The geodesic complexity of n-dimensional Klein bottles
• Geodesic complexity of the octahedron, and an algorithm for cut loci on convex polyhedra
• Geodesic complexity for non-geodesic spaces
• Geodesic complexity via fibered decompositions of cut loci