Transversality in elliptic Morse theory for the symplectic action

Abstract

Our goal in this paper is to settle some transversality question for the perturbed nonlinear Cauchy-Riemann equations on the cylinder. These results play a central role in the denition of symplectic Floer homology and hence in the proof of the Arnold conjecture. There is currently no other reference to these transversality results in the open literature. Our approach does not require Aronszajn’s theorem. Instead we derive the unique continuation theorem from a generalization of the Carleman similarity principle.