  In this paper, we present a generalisation of a theorem of David and Rob
Pollack. In 'A construction of rigid analytic cohomology classes for congruence
subgroups of SL(3,Z)', they give a very general argument for lifting ordinary
eigenclasses (with respect to a suitable operator) in the group cohomology of
certain arithmetic groups. With slightly tighter conditions, we prove the same
result for non-ordinary classes. Pollack and Pollack apply their results to the
case of p-ordinary classes in the group cohomology of congruence subgroups for
SL3, constructing explicit overconvergent classes in this setting. As an
application of our results, we give an extension of their results to the case
of non-critical slope classes in the same setting.
