Can we have a nontrivial linking of a $S^p$ sphere and a $S^q$ sphere in the $\mathbb{R}^d$ space (or in the ${S}^d$ space)? I suppose that it can happen only if $p+q<d$.
For example, we can have:
(1) $S^1$ and $S^1$ can be linked in $\mathbb{R}^3$ $\to$ True.
My question is that can we have:
(2) $S^2$ and $S^1$ can be linked in $\mathbb{R}^4$? $\to$ True?
(3) $S^1$ and $S^1$ can be linked in $\mathbb{R}^5$? $\to$ False?
(4) $S^1$ and $S^2$ can be linked in $\mathbb{R}^5$? $\to$ False?
(5) $S^1$ and $S^3$ can be linked in $\mathbb{R}^5$? $\to$ True?
(6) $S^2$ and $S^2$ can be linked in $\mathbb{R}^5$? $\to$ True?
And the answers are the same if we replace the $\mathbb{R}^d$ space by the ${S}^d$ space, correct?