  We consider the homotopy type of maps between symplectic surface whose graphs
form symplectic submanifolds of the product. We give a purely topological model
for this space in terms of maps with constrained numbers of pre-images. We use
this to show that the dependence of the homotopy type on the area forms of each
surface is quantized- it changes only when the parameters pass certain discrete
levels. When the domain is a sphere or torus, and its total area is smaller
than the range, we compute the full homotopy type of the low degree components.
We also give an example, showing that the homotopy type of the space of
sections of a symplectic fibration F must sometimes change as we deform F. Much
of this work generalizes to n-dimensional manifolds equipped with volume forms.
