Intrinsic linking and knotting are arbitrarily complex
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We show that, given any $n$ and $α$, 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 $i\not =j$, $|\lk(Q_i,Q_j)|\geqα$ and $|a_2(Q_i)|\geqα$, where $a_{2}(Q_i)$ denotes the second coefficient of the Conway polynomial of $Q_i$.
18 pages, 5 figures. Proposition 2 has been strengthened, and Corollary 1 and Proposition 3 have been added to answer a question of Taniyama's
18 pages, 5 figures. Proposition 2 has been strengthened, and Corollary 1 and Proposition 3 have been added to answer a question of Taniyama's