Let $i:T^{2}\rightarrow S^{1}\times S^{2}$ be an embedding map.
If $i(T^{2})$ is inseparable in $S^{1}\times S^{2}$, then $S^{1}\times S^{2}-i(T^{2})\cong (O\cup K)^{c}$. Here $(O\cup K)^{c}$ is a two components link complement in $S^{3}$ such that $O$ is a trivial knot and $K$ can be any unlinked with $O$.