A cobordism is called Lagrangian cobordism when L and L' are Lagrangians in a symplectic manifold (M, w) and W is an embedded Lagrangian in [0,1]* R * M with the property that near the boundary it looks like the products over L and L'. A Lagrangian pseudo-isotopy is a Lagrangian cobordism (W; L, L'), diffeomorphic to a trivial cobordism L*[0,1].
In this talk we will see that under some topological constraint an exact Lagrangian cobordism is Lagrangian pseudo-isotopy. We use Floer homology and the s-cobordism theorem.