By Milgram R.J.

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Figure 8 curve For n ≥ 2 we use the following construction. Start with D1n = {(x1 , . . , xn , 0, . . , 0) ∈ R2n | D2n = {(0, . . , 0, y1 , . . , yn ) ∈ R2n | x2i ≤ 1} , yi2 ≤ 1} . The intersection of the unit sphere S 2n+1 ⊂ R2n with D1n D2n , S 2n−1 ∩ D1n = S1n−1 , S 2n−1 ∩ D2n = S2n−1 is a pair of linked spheres in S 2n−1 . Next we connect them together by a tube in the complement of the unit ball.

Figure 8 curve For n ≥ 2 we use the following construction. Start with D1n = {(x1 , . . , xn , 0, . . , 0) ∈ R2n | D2n = {(0, . . , 0, y1 , . . , yn ) ∈ R2n | x2i ≤ 1} , yi2 ≤ 1} . The intersection of the unit sphere S 2n+1 ⊂ R2n with D1n D2n , S 2n−1 ∩ D1n = S1n−1 , S 2n−1 ∩ D2n = S2n−1 is a pair of linked spheres in S 2n−1 . Next we connect them together by a tube in the complement of the unit ball.