Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embeddability and quasi-isometric classification of partially
  commutative groups   The main goal of this note is to suggest an algebraic approach to the
quasi-isometric classification of partially commutative groups (alias
right-angled Artin groups). More precisely, we conjecture that if the partially
commutative groups $\mathbb{G}(\Delta)$ and $\mathbb{G}(\Gamma)$ are
quasi-isometric, then $\mathbb{G}(\Delta)$ is a (nice) subgroup of
$\mathbb{G}(\Gamma)$ and vice-versa. We show that the conjecture holds for all
known cases of quasi-isometric classification of partially commutative groups,
namely for the classes of $n$-tress and atomic graphs.
  As in the classical Mostow rigidity theory for irreducible lattices, we
relate the quasi-isometric rigidity of the class of atomic partially
commutative groups with the algebraic rigidity, that is with the co-Hopfian
property of their $\mathbb{Q}$-completions.

29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th