• What is a handle-slide? Oszvath-Szabo has a nice article here.
• How do we see if the two Lagrangian torus are equivalent or not?

His 2011 talk slide on the big pictures.

We are building 4d TFT, which should assign a number to a closed 4-manifold. a vector space (or graded abelian group) to a closed 3-manifold, and a category to a closed 2-manifold. Moreover, for a cobordism of 3-manifolds $Y_0^3 \leadsto Y_1^3$ by $W^4$, we have a homomorphism from $Z(W): Z(Y_0) \to Z(Y_1)$. For a cobordism $Y: \Sigma_1 \leadsto \Sigma_2$, we have a functor $Z(Y): Z(\Sigma_1) \to Z(\Sigma_2)$.