On the Topology of Celtic Knot Designs
Intrinsic linking and knotting are arbitrarily complex
We show that, given any n and α, any embedding of any sufficiently large complete graph in ℝ³ contains an oriented link with components Q₁, ..., Qₙ such that for every i ≠ j, and , where denotes the second coefficient of the Conway polynomial of .
Symmetries of embedded complete bipartite graphs
We characterize which automorphisms of an arbitrary complete bipartite graph can be induced by a homeomorphism of some embedding of the graph in S³.
A geometric interpretation of Milnor's triple linking numbers.
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