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 that this extends to arbitrary dimensions. In
dimensions where this holds, the set of deformation classes of
hyperpencils canonically maps onto the set of isotopy classes
of rational symplectic forms up to positive scale, topologically
determining a dense subset of all symplectic forms up to an
equivalence relation on hyperpencils. In particular, the existence
of a hyperpencil topologically characterizes those manifolds
in dimensions ≤ 6 (and perhaps in general) that admit
symplectic structures.