We describe an operation which modifies a Lagrangian submanifold $L$ in a symplectic manifold $(M, \omega)$ such as to produce a new immersed Lagrangian submanifold $L'$, which as a smooth manifold is obtained by surgery along a framed sphere in $L$. Intuitively, this can be described as collapsing an isotropic disc with boundary on $L$ to a point. The inverse operation generalizes classical Lagrangian surgery. We also describe corresponding immersed Lagrangian cobordisms between $L$ and $L'$ . After removal of their singular locus, we obtain examples of embedded Lagrangian cobordisms with precisely two ends. As an application, we use this construction to produce interesting examples of Lagrangian cobordisms between Clifford and Chekanov tori.

中文翻译：

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拉格朗日抗手术

我们描述了一种修改辛流形 $(M, \omega)$ 中的拉格朗日子流形 $L$ 的操作，例如产生一个新的浸入式拉格朗日子流形 $L'$，它作为平滑流形是通过沿着框架的手术获得的以 $L$ 为单位的球体。直观地说，这可以描述为将边界在 $L$ 上的各向同性圆盘塌陷成一个点。逆运算推广了经典的拉格朗日手术。我们还描述了 $L$ 和 $L'$ 之间相应的浸入式拉格朗日坐标。去除它们的奇异轨迹后，我们获得了具有精确两端的嵌入拉格朗日坐标的例子。作为一个应用，我们使用这种结构来生成 Clifford 和 Chekanov tori 之间的拉格朗日协边的有趣例子。