  In this paper we obtain the complete classification of the inequivalent
classes of M2-brane symplectic torus bundles with monodromy in $SL(2,Z)$ and
their precise U-duality relations among them. There are eight inequivalent
classes of bundles whose monodromy groups, at low energies, are in
correspondence with the gauging groups of the eight type II gauged
supergravities in nine dimensions. Four of those have been previously found and
they correspond to the 'type IIB side'. In this paper we provide the explicit
realization of the remaining four classes associated to the 'type IIA side'.
The precise M2-brane U-duality relations between the eight inequivalent classes
of bundles have allowed to identified the remaining four ones. We conjecture
that the classes of gaugings -- classifying the eight types of II gauged
supergravity in nine dimensions -- are determined by the inequivalent
coinvariant classes associated to the base and the fiber of the supermembrane
bundles and their duals.
