Local symplectic field theory

TL;DR

This paper introduces a local version of symplectic field theory extending local Gromov-Witten theory, with results on transversality and algebraic structures in four-dimensional cases with cylindrical ends.

Contribution

It defines a new local symplectic field theory framework and proves transversality for multiple covers in specific four-dimensional settings.

Findings

Transversality established for multiple covers in four-dimensional cases.

Algebraic structures derived from the local symplectic field theory.

Extension of local Gromov-Witten theory to symplectic field theory.

Abstract

Generalizing local Gromov-Witten theory, in this paper we define a local version of symplectic field theory. When the symplectic manifold with cylindrical ends is four-dimensional and the underlying simple curve is regular by automatic transversality, we establish a transversality result for all its multiple covers and discuss the resulting algebraic structures.