Symplectic Classes on Elliptic Surfaces I

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 without multiple fibers.

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