Obstructions to matricial stability of discrete groups and almost flat K-theory

A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of are perturbable to genuine in point-norm topology. For large classes groups G, we show that matricial stability implies vanishing rational cohomology all nonzero even dimensions. We revisit a method constructing almost flat K-theory BG which involves dual assembly map and quasidiagonality properties G. The existence not represents an obstruction due continuity monodromy correspondence.