Transversality in elliptic Morse theory for the symplectic action

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 definition 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 Aronszajns theorem. Instead we derive the unique continuation theorem from a generalization of the Carleman similarity principle. A. Floer died on May 15th, 1991 1 Introduction Let (M; !) be a compact symplectic manifold and consider the differential equation x (t) = X t (x (t) ) (1) where X t = X t+1: M ! TM is a smooth family of symplectic vector fields, i. e. the 1-forms (X t) ! are closed. The periodic solutions x (t) = x (t + 1) of (1) are the zeros of the closed 1-form \ X on the loop space L of M defined by \ X (x; ¸) = Z 1 0 ! (x (t) \ X t (x (t) ) ; ¸ (t) ) dt for ¸ 2 T x L = C 1. . .