Physical Sciences and Mathematics Commons^™

Intrinsic Linking And Knotting Are Arbitrarily Complex, Erica Flapan, Blake Mellor, Ramin Naimi

Mathematics Faculty Works

We show that, given any n and α, every embedding of any sufficiently large complete graph in R³ contains an oriented link with components Q₁, ..., Q_n such that for every i≠j, $|\lk(Q_i,Q_j)|\geq\alpha$ and |a₂(Qi)|≥α, where a₂(Q_i) denotes the second coefficient of the Conway polynomial of Q_i.