Boletin de la Sociedad Matematica Mexicana, volume 30, issue 2, publication number 38
Geodesic complexity of a cube
Donald M Davis
1
Publication type: Journal Article
Publication date: 2024-04-10
scimago Q2
SJR: 0.399
CiteScore: 1.6
Impact factor: 0.9
ISSN: 00378615, 1405213X, 22964495
General Mathematics
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 3-dimensional cube exceeds its topological complexity by exactly 2. The proof involves a careful analysis of cut loci of the cube.
Found
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