-- CANCELLED -- Embedded Lagrangian fillings not coming from surgery

Let $\Lambda$ be a Legendrian knot or link in the standard 3-dimensional contact space, and let $\Sigma$ be an immersed Lagrangian filling of $\Lambda$ in the symplectization. Polterovich (or Lagrangian) surgery permits to solve immersed points to get embedded Lagrangian surfaces, each solved double point increasing the genus by one. We ask if this procedure is reversible: can any Lagrangian filling $\Sigma$ with genus $g(\Sigma)>0$ and $i(\Sigma)$ immersed points be obtained from surgery on a Lagrangian filling $\Sigma'$ with $g(\Sigma')=g(\Sigma)-1$ and $i(\Sigma')=i(\Sigma)+1$? We will see that the answer is no and give counter-examples. This is work in progress, joint with O. Capovilla-Searle, N. Legout, E. Murphy, Y. Pan and L. Traynor.