Floer cohomology in the simplest case

From Talbot

Here, we want to see Floer cohomology for Lagrangian submanifolds in the exact (or maybe symplectically aspherical, if you really want) case. This can follow Floer's original paper or (Seidel, book). It should include a discussion of the action functional and the definition of the differential, with a sketch of d^2 = 0. We don't have bubbling so things are easy. We also want to mention that HF(L,L) = H(L).

One example where things can be made explicit is where M = cotangent bundle, L_0 = zero-section, L_1 = graph(df). In that case, another paper by Floer ("Witten's complex..") actually determines the differential completely, for a suitably chosen almost complex structure, in terms of Morse theory.

You also will want to mention Gromov's original application: there are no compact exact Lagrangian submanifolds in R^{2n}.

Floer cohomology for Hamiltonian fixed points does not enter into Talbot, so I think we should not discuss it at all.