Intrinsic linking and knotting are arbitrarily complex

Volume 201 / 2008

Erica Flapan, Blake Mellor, Ramin Naimi 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 $Q_i$.

Authors

  • Erica FlapanDepartment of Mathematics
    Pomona College
    Claremont, CA 91711, U.S.A.
    e-mail
  • Blake MellorDepartment of Mathematics
    Loyola Marymount University
    Los Angeles, CA 90045, U.S.A.
    e-mail
  • Ramin NaimiDepartment of Mathematics
    Occidental College
    Los Angeles, CA 90041, U.S.A.
    e-mail

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