Uniform property Γ

We further examine the concept of uniform property Gamma for C*-algebras
introduced in our joint work with Winter. In addition to obtaining
characterisations in the spirit of Dixmier's work on central sequence in II$_1$
factors, we establish the equivalence of uniform property Gamma, a suitable
uniform version of McDuff's property for C*-algebras, and the existence of
complemented partitions of unity for separable nuclear C*-algebras with no
finite dimensional representations and a compact (non-empty) tracial state
space. As a consequence, for C*-algebras as in the Toms-Winter conjecture, the
combination of strict comparison and uniform property Gamma is equivalent to
Jiang-Su stability. We also show how these ideas can be combined with those of
Matui-Sato to streamline Winter's classification-by-embeddings technique.