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

TL;DR

This paper develops a moduli theory for pseudo holomorphic curves in infinite-dimensional almost Kaehler manifolds formed by sequences, extending finite-dimensional techniques through a functional analytic framework.

Contribution

It introduces a new approach to analyze pseudo holomorphic curves in infinite-dimensional high-symmetry almost Kaehler manifolds, bridging finite and infinite-dimensional moduli theories.

Findings

Established a functional analytic framework for infinite-dimensional moduli spaces

Extended standard pseudo holomorphic curve techniques to infinite-dimensional settings

Demonstrated applicability to high-symmetry almost Kaehler manifolds

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.