Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Complex of Affinely Commutative Sets   We show that for some classes of groups $G$, the homotopy fiber
$E_{\mathrm{com}} G$ of the inclusion of the classifying space for
commutativity $E_{\mathrm{com}} G$ into the classifying space $BG$, is
contractible if and only if $G$ is abelian. We show this both for compact
connected Lie groups and for discrete groups. To prove those results, we define
an interesting map $\mathfrak{c} \colon E_{\mathrm{com}} G \to B[G,G]$ and show
it is not nullhomotopic for the non-abelian groups in those classes.
Additionally, we show that $\mathfrak{c}$ is 3-connected for $G=O(n)$ when $n
\ge 3$.

9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat