  In this paper, we prove homological stability of symplectomorphisms and
extended hamiltonians of surfaces made discrete. We construct an isomorphism
from the stable homology group of symplectomorphisms and extended Hamiltonians
of surfaces to the homology of certain infinite loop spaces. We use these
infinite loop spaces to study characteristic classes of surface bundles whose
holonomy groups are area preserving, in particular we give a homotopy theoretic
proof of the Kotschick-Morita theorem.

Algebraic Topology;Geometric Topology;Symplectic Geometry