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Given an immersed, Maslov-$0$, exact Lagrangian filling of a Legendrian knot,if the filling has a vanishing index and action double point, then throughLagrangian surgery it is possible to obtain a new immersed, Maslov-$0$, exactLagrangian filling with one less double point and with genus increased by one.We show that it is not always possible to reverse the Lagrangian surgery: notevery immersed, Maslov-$0$, exact Lagrangian filling with genus $g \geq 1$ and$p$ double points can be obtained from such a Lagrangian surgery on a fillingof genus $g-1$ with $p+1$ double points. To show this, we establish theconnection between the existence of an immersed, Maslov-$0$, exact Lagrangianfilling of a Legendrian $\Lambda$ that has $p$ double points with action $0$and the existence of an embedded, Maslov-$0$, exact Lagrangian cobordism from$p$ copies of a Hopf link to $\Lambda$. We then prove that a count ofaugmentations provides an obstruction to the existence of embedded, Maslov-$0$,exact Lagrangian cobordisms between Legendrian links.

Obstructions to reversing Lagrangian surgery in Lagrangian fillings