Geodesic
Intrinsic linking and knotting are arbitrarily complex
Erica Flapan 1   ; Blake Mellor 2   ; Ramin Naimi 3
1 Department of Mathematics Pomona College Claremont, CA 91711, U.S.A.
2 Department of Mathematics Loyola Marymount University Los Angeles, CA 90045, U.S.A.
3 Department of Mathematics Occidental College Los Angeles, CA 90041, U.S.A.
Fundamenta Mathematicae, Tome 201 (2008) no. 2, pp. 131-148 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $Q_i$.
DOI : 10.4064/fm201-2-3
Keywords: given alpha embedding sufficiently large complete graph mathbb contains oriented link components ldots every j geq alpha geq alpha where denotes second coefficient conway polynomial

Erica Flapan  1   ; Blake Mellor  2   ; Ramin Naimi  3

1 Department of Mathematics Pomona College Claremont, CA 91711, U.S.A.
2 Department of Mathematics Loyola Marymount University Los Angeles, CA 90045, U.S.A.
3 Department of Mathematics Occidental College Los Angeles, CA 90041, U.S.A. 
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Erica Flapan; Blake Mellor; Ramin Naimi. Intrinsic linking and knotting are arbitrarily complex. Fundamenta Mathematicae, Tome 201 (2008) no. 2, pp. 131-148. doi: 10.4064/fm201-2-3

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