linking, knotting, Conway polynomial
We show that, given any n and alpha, any embedding of any sufficiently large complete graph in R3 contains an oriented link with components Q1,...,Qn such that for every i not equal to j, Ilk(Qi,Qj)I greater than or equal to alpha and la2(Qi)l greater than or equal to alpha, where a2(Qi) denotes the second coefficient of the Conway polynomial of Qi.
© Instytut Matematyczny PAN, 2008
E. Flapan, B. Mellor, and R. Naimi, Intrinsic Linking and Knotting are Arbitrarily Complex, Fundamenta Mathematicae, Vol 201 (2008),131-148.
Final published version can be found at:
E. Flapan, B. Mellor, and R. Naimi, Intrinsic Linking and Knotting are Arbitrarily Complex, Fundamenta Mathematicae, Vol 201 (2008),131-148. doi:10.4064/fm201-2-3
Or at the following link: https://www.impan.pl/en/publishing-house/journals-and-series/fundamenta-mathematicae/all/201/2/89035/intrinsic-linking-and-knotting-are-arbitrarily-complex