Non-displaceable Lagrangian links in four-manifolds

Let $ω$ denote an area form on $S^2$. Consider the closed symplectic 4-manifold $M=(S^2\times S^2, Aω\oplus a ω)$ with $0<a<A$. We show that there are families of displaceable Lagrangian tori $L_{0,x},\, L_{1,x} \subset M$, for $x \in [0,1]$, such that the two-component link $L_{0,x} \cup L_{1,x}$ is non-displaceable for each $x$.

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