Intrinsic linking and knotting are arbitrarily complex

Erica Flapan; Blake Mellor; Ramin Naimi

Intrinsic linking and knotting are arbitrarily complex

Erica Flapan, Blake Mellor, Ramin Naimi

Research output: Contribution to journal › Article › peer-review

Abstract

We show that, given any n and α, every embedding of any sufficiently large complete graph in R ³ contains an oriented link with components Q ₁ , ..., Q _n such that for every i≠j, $|\lk(Q_i,Q_j)|\geq\alpha$ and |a ₂ (Qi)|≥α, where a ₂ (Q _i ) denotes the second coefficient of the Conway polynomial of Q _i .

Original language	American English
Pages (from-to)	131-148
Journal	Fundamenta Mathematicae
Volume	201
Issue number	2
State	Published - 2008

Keywords

intrinsically linked graphs
intrinsically knotted graphs

Disciplines

Discrete Mathematics and Combinatorics
Geometry and Topology

Cite this

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title = "Intrinsic linking and knotting are arbitrarily complex",

abstract = " We show that, given any n and α, every embedding of any sufficiently large complete graph in R 3 contains an oriented link with components Q 1 , ..., Q n such that for every i≠j, $|\lk(Q_i,Q_j)|\geq\alpha$ and |a 2 (Qi)|≥α, where a 2 (Q i ) denotes the second coefficient of the Conway polynomial of Q i .",

keywords = "intrinsically linked graphs, intrinsically knotted graphs",

author = "Erica Flapan and Blake Mellor and Ramin Naimi",

note = "Flapan, E., B. Mellor, and R. Naimi, 2008: Intrinsic linking and knotting are arbitrarily complex. Fundamenta Mathematicae, 201.2, 131-148, arXiv:math/0610501.",

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journal = "Fundamenta Mathematicae",

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T1 - Intrinsic linking and knotting are arbitrarily complex

AU - Flapan, Erica

AU - Mellor, Blake

AU - Naimi, Ramin

N1 - Flapan, E., B. Mellor, and R. Naimi, 2008: Intrinsic linking and knotting are arbitrarily complex. Fundamenta Mathematicae, 201.2, 131-148, arXiv:math/0610501.

PY - 2008

Y1 - 2008

N2 - We show that, given any n and α, every embedding of any sufficiently large complete graph in R 3 contains an oriented link with components Q 1 , ..., Q n such that for every i≠j, $|\lk(Q_i,Q_j)|\geq\alpha$ and |a 2 (Qi)|≥α, where a 2 (Q i ) denotes the second coefficient of the Conway polynomial of Q i .

AB - We show that, given any n and α, every embedding of any sufficiently large complete graph in R 3 contains an oriented link with components Q 1 , ..., Q n such that for every i≠j, $|\lk(Q_i,Q_j)|\geq\alpha$ and |a 2 (Qi)|≥α, where a 2 (Q i ) denotes the second coefficient of the Conway polynomial of Q i .

KW - intrinsically linked graphs

KW - intrinsically knotted graphs

UR - https://digitalcommons.lmu.edu/math_fac/34

M3 - Article

VL - 201

SP - 131

EP - 148

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

IS - 2

ER -

Intrinsic linking and knotting are arbitrarily complex

Abstract

Keywords

Disciplines

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Cite this