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

24 Jul 2020  ·  Marius Dadarlat ·

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

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Operator Algebras Group Theory K-Theory and Homology