Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Krein-Milman theorem for the space of sofic representations   Denote by $Sof(G)$ the space of sofic representations of a countable group
$G$. This space is known by a result of the second author, to have a
convex-like structure. We show that, in this space, minimal faces are extreme
points. We then construct uncountable many extreme points for
$Sof(\mathbb{F}_2)$ and show that there exists a decreasing chain of closed
faces with empty intersection. Finally we construct a strangely looking sofic
representation in $Sof(\mathbb{F}_2)$ that we believe it is outside of the
closure of the convex hull of extreme points.

22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex