Can we embed $S^{p} \times S^q$ in $S^d$ with all the nice properties, what are the allowed values of $p$ and $q$ for $d=2,3,4$ where $p+q \leq d$?
=For $d=2$=
I suppose that we cannot embed $S^{1} \times S^1$ in $S^2$.
=For $d=3$=
Can we embed $S^{2} \times S^1$ in $S^3$?
=For $d=4$=
Can we embed $S^{1} \times S^3$ in $S^4$?
Can we embed $S^{2} \times S^2$ in $S^4$?
Can we embed $S^{1} \times S^2$ in $S^4$? Yes?
Can we embed $S^{1} \times S^1 \times S^1$ in $S^4$? Yes?
What are the proofs and explanations?