  A discrete group is matricially stable if every function from the group to a
complex unitary group that is "almost multiplicative" in the point-operator
norm topology is "close" to a genuine unitary representation. It follows from a
recent result due to Dadarlat that all amenable, groups with non-torsion
integral 2-cohomology are not matricially stable, but the proof does not lead
to explicit examples of asymptotic representations that are not perturbable to
genuine representations. The purpose of this paper is to give an explicit
formula, in terms of cohomological data, for asymptotic representations that
are not perturbable to genuine representations for a class of groups that
contains all finitely generated groups with a non-torsion 2-cohomology class
that corresponds to a central extension where the middle group is residually
finite. This class includes polycyclic groups with non-torsion 2-cohomology.

Group Theory;K-Theory and Homology;Operator Algebras