Intrinsic linking and knotting are arbitrarily complex
Volume 201 / 2008
Fundamenta Mathematicae 201 (2008), 131-148
MSC: 57M25, 57M15, 05C10.
DOI: 10.4064/fm201-2-3
Abstract
We show that, given any $n$ and $\alpha$, any embedding of any sufficiently large complete graph in $\mathbb{R}^3$ contains an oriented link with components $Q_1, \ldots, Q_n$ such that for every $i\not =j$, $|{\rm lk}(Q_i,Q_j)|\geq\alpha$ and $|a_2(Q_i)|\geq\alpha$, where $a_{2}(Q_i)$ denotes the second coefficient of the Conway polynomial of $Q_i$.
