Symplectic Classes on Elliptic Surfaces with positive Euler Number

TL;DR

This paper characterizes the symplectic cone of elliptic surfaces with positive Euler number, a key invariant in understanding symplectic structures on 4-manifolds.

Contribution

It provides a description of the symplectic cone for elliptic surfaces with positive Euler number, advancing knowledge of symplectic classes on these manifolds.

Findings

Describes the symplectic cone for elliptic surfaces with positive Euler number.

Identifies the cohomology classes admitting symplectic representatives.

Contributes to understanding symplectic invariants of 4-manifolds.

Abstract

A key question for $4$-manifolds $M$ admitting symplectic structures is to determine which cohomology classes $\alpha\in H^2(M,\mathbb R)$ admit a symplectic representative. The collection of all such classes, the symplectic cone $\mathcal C_M$, is a basic smooth invariant of $M$. This paper describes the symplectic cone for elliptic surfaces with positive Euler number.