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 \(\mathcal {L}_{0,x},\, \mathcal {L}_{1,x} \subset M\), for \(x \in [0,1]\), such that the two-component link \(\mathcal {L}_{0,x} \cup \mathcal {L}_{1,x}\) is non-displaceable for each x.

中文翻译：

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四流形上不可移位的拉格朗日链

令\（\ omega \）表示\（S ^ 2 \）上的区域形式。考虑封闭辛4流形\（M =（S ^ 2 \乘以S ^ 2，A \ omega \ oplus一个\ omega）\）与\（0 <a <A \）。我们表明，有移动的拉格朗日托里的家庭\（\ mathcal {L} _ {0，X}，\，\ mathcal {L} _ {1，X} \子集中号\），用于\（X \在[ 0,1] \），这样两个分量链接\（\ mathcal {L} _ {0，x} \ cup \ mathcal {L} _ {1，x} \）对于每个x都是不可移位的。