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Intrinsic linking and knotting are arbitrarily complex

Erica FlapanBlake MellorRamin Naimi — 2008

Fundamenta Mathematicae

We show that, given any n and α, any embedding of any sufficiently large complete graph in ℝ³ contains an oriented link with components Q₁, ..., Qₙ such that for every i ≠ j, | l k ( Q i , Q j ) | α and | a ( Q i ) | α , where a ( Q i ) denotes the second coefficient of the Conway polynomial of Q i .

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