Gromov Witten invariants of exploded manifolds

TL;DR

This paper develops a framework for defining Gromov Witten invariants within exploded manifolds, including relative invariants and a gluing theorem, advancing the understanding of holomorphic curves in this setting.

Contribution

It introduces the construction of Gromov Witten invariants in exploded manifolds, including relative invariants and a gluing theorem, expanding the scope of symplectic geometry.

Findings

Defined Gromov Witten invariants relative to normal crossing divisors

Proved a gluing theorem involving tropical curves

Established a structure for the moduli space of holomorphic curves in exploded manifolds

Abstract

This paper describes the structure of the moduli space of holomorphic curves and constructs Gromov Witten invariants in the category of exploded manifolds. This includes defining Gromov Witten invariants relative to normal crossing divisors and proving the associated gluing theorem which involves summing relative invariants over a count of tropical curves.