For $a,b> 0$, define the symplectic polydisk $P(a,b)\subset \mathbb{C}^2$ as the set of points $(z_1,z_2)$ s.t. $$|z_1|^2\leq a, |z_1|^2\leq b.$$ Notice that the boundary of $P(a,b)$ is topologically $S^3$.
I would like to know, topollogically speaking, what is the boundary of $P(2,1)\cup P(1,2)$. I know that is either $S^3$ or a solid torus with its 2-dim boundary, but it is still not clear to me which one of those. I would appreciate any insight.