Representing homology classes by symplectic surfaces

TL;DR

This paper introduces an obstruction criterion for representing homology classes in symplectic 4-manifolds with embedded symplectic surfaces, addressing the existence problem in symplectic topology.

Contribution

It provides a new obstruction condition that limits when a homology class can be represented by a symplectic surface in 4-manifolds.

Findings

Obstruction criterion for symplectic surface representation

Limits on representing homology classes by symplectic surfaces

Advances understanding of symplectic embedding problems

Abstract

We derive an obstruction to representing a homology class of a symplectic 4-manifold by an embedded, possibly disconnected, symplectic surface.