Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Bieri-Neumann-Strebel-Renz invariants of the weak commutativity
  construction $\X(G)$   For a finitely generated group $G$ we calculate the
Bieri-Neumann-Strebel-Renz invariant $\Sigma^1(\X(G))$ for the weak
commutativity construction $\X(G)$. Identifying $S(\X(G))$ with $S(\X(G) /
W(G))$ we show $\Sigma^2(\X(G),\Z) \subseteq \Sigma^2(\X(G)/ W(G),\Z)$ and
$\Sigma^2(\X(G)) \subseteq $ $ \Sigma^2(\X(G)/ W(G))$ that are equalities when
$W(G)$ is finitely generated and we explicitly calculate $\Sigma^2(\X(G)/
W(G),\Z)$ and $ \Sigma^2(\X(G)/ W(G))$ in terms of the $\Sigma$-invariants of
$G$. We calculate completely the $\Sigma$-invariants in dimensions 1 and 2 of
the group $\nu(G)$ and show that if $G$ is finitely generated group with
finitely presented commutator subgroup then the non-abelian tensor square $G
\otimes G$ is finitely presented.

15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con