A note on geometric duality in matroid theory and knot theory
arXiv:2110.01551
Abstract
We observe that for planar graphs, the geometric duality relation generates both 2-isomorphism and abstract duality. This observation has the surprising consequence that for links, the equivalence relation defined by isomorphisms of checkerboard graphs is the same as the equivalence relation defined by 2-isomorphisms of checkerboard graphs.
v1: 10 pages, 6 figures. v2: minor edits. v3: 11 pages, 6 figures. final prepublication version