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Quantum algebra and the Four Color Theorem
by
Paul Kainen
Georgetown University
It is shown that the Four Color Theorem (4CT) provides a natural connection between quantum algebra and physics. In particular, the natural operation which relates two edge 3-colored rooted cubic plane trees by an elementary ``associational switch'' surgery is characterized by inducing a zero-mapping between iterated tensor products of the usual qubit space (a complex vector space of complex dimension 2). But the 4CT is actually equivalent to a combinatorial rule for propagating twisting force, so a connection between physics and quantum algebra manifestly does exist. An application of the quaternions shows that in extending a coloring from one rooted cubic plane tree to another, the extension cannot fail on the last step.
Date received: May 5, 2003
Copyright © 2003 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # calc-19.