A note on geometric duality in matroid theory and knot theory (Q2166225)

The author establishes in this paper the observation 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.'' Despite this fact, the author proves that geometric duality suffices to define abstract duality of planar graphs. Moreover, he shows that geometric duality also suffices to define 2-isomorphism of planar graphs.