HYPERKÄHLER ARNOLD CONJECTURE AND ITS GENERALIZATIONS

Abstract

We generalize and refine the hyperkähler Arnold conjecture, which was originally established, in the non-degenerate case, for three-dimensional time by Hohloch, Noetzel and Salamon by means of hyperkähler Floer theory. In particular, we prove the conjecture in the case where the time manifold is a multidimensional torus and also establish the degenerate version of the conjecture. Our method relies on Morse theory for generating functions and a finite-dimensional reduction along the lines of the Conley–Zehnder proof of the Arnold conjecture for the torus.