Obstructions to Lagrangian surgery

Given a Lagrangian immersion with a transverse double point, we can surger this point to obtain an embedded Lagrangian with more complicated topology. As a classical example, both the Clifford and Chekanov tori in C² are obtained via Lagrangian surgery on a immersed sphere called the Whitney sphere. In the talk we'll discuss a Floer-theoretic obstruction to this: that is, showing that a Lagrangian cannot be realized as a surgery. An interesting dilemma is that PH invariants of an immersed Lagrangian itself cannot detect the fact that it is immersed. Instead, we have to consider families of Floer invariants coming from all possible surgeries, and use properties specific to SFT Lagrangian cobordism maps.