Is it possible to have linked n-spheres in any other space other than $\Bbb R^{n+2}$?

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Two $n$-spheres can be linked in infinitely many ways in $\Bbb R^{n+2}$? Is it possible to have two n-spheres tamely linked in $\Bbb R^{n+1}$?

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I’m not sure exactly what you are looking for since you don’t wish to limit the notion of linking. Would you consider two Alexander horned spheres in $\mathbb R^3$ whose ‘arms’ are ‘interlocked’ at the first level of iteration but with distinct Cantor sets at the end of the construction to be linked? If so, that’s your answer. If not, please tell us more about the question.