Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity properties in the classification program for separable
  amenable C*-algebras   We report on recent progress in the program to classify separable amenable
C*-algebras. Our emphasis is on the newly apparent role of regularity
properties such as finite decomposition rank, strict comparison of positive
elements, and Z-stability, and on the importance of the Cuntz semigroup. We
include a brief history of the program's successes since 1989, a more detailed
look at the Villadsen-type algebras which have so dramatically changed the
landscape, and a collection of announcements on the structure and properties of
the Cuntz semigroup.

22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th