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Toward a topological characterization of symplectic manifolds
The Journal of Symplectic Geometry
A fibration-like structure called a hyperpencil is defined on a smooth, closed 2n-manifold X, generalizing a linear system of curves on an algebraic variety. A deformation class of hyperpencils is shown to determine an isotopy class of symplectic structures on X. This provides an inverse to Donaldson's program for constructing linear systems on symplectic manifolds. In dimensions ≤ 6, work of Donaldson and Auroux provides hyperpencils on any symplectic manifold, and the author conjectures thatdoi:10.4310/jsg.2004.v2.n2.a1 fatcat:wmxzm6snefeldged36aujwz5fu