Non-displaceable Lagrangian links in four-manifolds

Abstract

Let $\omega$ denote an area form on $S^2$. Consider the closed symplectic 4-manifold $M=(S^2\times S^2,A\omega \oplus a\omega )$ 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 $x$.

37 pages, to appear in GAFA