Symplectic Classes on Elliptic Surfaces I

2025/07/28 by Dorfmeister, Josef G., Li, Tian-Jun
#Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2507.20940

Abstract

A key question for 4-manifolds M admitting symplectic structures is to determine which cohomology classes α∈ H²(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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