Transversality in elliptic Morse theory for the symplectic action (Q1908594)

The goal of this paper is to settle some transversality questions for the perturbed nonlinear Cauchy-Riemann equations on the cylinder. These results play a central role in the definition of symplectic Floer homology and hence in the proof of the Arnold conjecture. The precise definition involves an infinite-dimensional analogue of Witten's approach to Morse theory. In the finite-dimensional context, this construction requires the Morse-Smale transversality condition, namely, that the stable and unstable manifolds of any two critical points intersect transversally. The infinite-dimensional analogue of this condition is presented in the paper.