Abstract:Let n, q and r be positive integers, and let K n N be the n-skeleton of an (N − 1)-simplex. We show that for N sufficiently large every embedding of K n N in R 2n+1 contains a link L 1 ∪ · · · ∪ L r consisting of r disjoint n-spheres, such that the linking number ℓk(L i , L j ) is a nonzero multiple of q for all i = j. This result is new in the classical case n = 1 (graphs embedded in R 3 ) as well as the higher dimensional cases n ≥ 2; and since it implies the existence of a link L 1 ∪ · · · ∪ L r such that |… Show more
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