Complementary Regions of Knot and Link Diagrams

Details Complementary Regions of Knot and Link Diagrams Complementary Regions of Knot and Link Diagrams

2008-12-13

arxiv.org/abs/0812.2558v1

Mathematics

Geometric Topology

16 pages, 17 figures

Scientific paper

An increasing sequence of integers is said to be universal for knots and links if every knot and link has a projection to the sphere such that the number of edges of each complementary face of the projection comes from the given sequence. This paper is an investigation into which sequences, either finite or infinite, are universal. We also consider how to minimize the number of odd-sided faces for projections of knots and links with n components.

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