# Uniform property Γ

Castillejos, J
Evington, S
Tikuisis, A
White, S

13 February 2021

## Journal:

International Mathematics Research Notices

## Last Updated:

2021-10-19T13:23:46.017+01:00

## DOI:

10.1093/imrn/rnaa282

## abstract:

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.

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