Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The homotopy theory of polyhedral products associated with flag
  complexes   If $K$ is a simplicial complex on $m$ vertices the flagification of $K$ is
the minimal flag complex $K^f$ on the same vertex set that contains $K$.
Letting $L$ be the set of vertices, there is a sequence of simplicial
inclusions $L\to K\to K^f$. This induces a sequence of maps of polyhedral
products $(\underline X,\underline A)^L\stackrel g\longrightarrow(\underline
X,\underline A)^K\stackrel f\longrightarrow (\underline X,\underline A)^{K^f}$.
We show that $\Omega f$ and $\Omega f\circ\Omega g$ have right homotopy
inverses and draw consequences. For a flag complex $K$ the polyhedral product
of the form $(\underline{CY},\underline Y)^K$ is a co-$H$-space if and only if
the $1$-skeleton of $K$ is a chordal graph, and we deduce that the maps $f$ and
$f\circ g$ have right homotopy inverses in this case.

4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
3
The categories of this paper are: physics
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol