Intrinsic linking and knotting are arbitrarily complex

Details Intrinsic linking and knotting are arbitrarily complex Intrinsic linking and knotting are arbitrarily complex

2006-10-16

arxiv.org/abs/math/0610501v6

Fund. Math., vol. 201, no. 2, 2008, pp. 131-148

Mathematics

Geometric Topology

18 pages, 5 figures. Proposition 2 has been strengthened, and Corollary 1 and Proposition 3 have been added to answer a questi

Scientific paper

We show that, given any $n$ and $\alpha$, every embedding of any sufficiently
large complete graph in $\mathbb{R}^3$ contains an oriented link with
components $Q_1$, ..., $Q_n$ such that for every $i\not =j$,
$|\lk(Q_i,Q_j)|\geq\alpha$ and $|a_2(Q_i)|\geq\alpha$, where $a_{2}(Q_i)$
denotes the second coefficient of the Conway polynomial of $Q_i$.

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