Infinite sequences of almost Kaehler manifolds with high symmetry, their perturbations and pseudo holomorphic curves

Abstract

We study analysis over infinite dimensional manifolds consisted by sequences of almost Kaehler manifolds. We develop moduli theory of pseudo holomorphic curves into such spaces with high symmetry. Many mechanisms of the standard moduli theory over finite dimensional spaces also work over these infinite dimensional spaces, which is based on a simple functional analytic framework.