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Complementary Regions of Knot and Link Projections
by
Colin Adams
Williams College
Coauthors: Reiko Shinjo, Kokoro Tanaka
A strictly increasing sequence of integers is said to be universal if every knot can be realized by a projection, the complementary regions of which are n-gons, for values of n that occur in the list. We prove that (2, n, n+1, ...) for n ≥ 3 and (3, n, n+1, ...) for n ≥ 4 are universal. Moreover, (3, 4, n) is universal for all n ≥ 5, and (2, 4, 5) is universal. We also consider sequences for n-component links.
Date received: November 17, 2008
Copyright © 2008 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 # caxq-24.