Integral counts of pseudo-holomorphic curves

TL;DR

This paper provides detailed construction methods for counting pseudo-holomorphic curves in compact symplectic and exploded manifolds, aiming to produce integer-valued invariants as proposed by Fukaya and Ono.

Contribution

It offers a comprehensive implementation of Fukaya and Ono's approach for a broad class of manifolds, filling in the details of their original outline.

Findings

Constructs integer-valued invariants from pseudo-holomorphic curves

Extends Fukaya and Ono's method to exploded manifolds

Provides detailed proofs and methodology

Abstract

In \cite{FOinteger}, Fukaya and Ono outlined a way of counting pseudo-holomorphic curves in a general compact symplectic manifold to obtain integer valued invariants. This paper contains the details of Fukaya and Ono's suggested construction for any compact symplectic manifold and a large class of exploded manifolds.