论文标题
在Bieri-Neumann-Strebel-Renz上不变的薄弱通勤构建$ \ x（g）$
On the Bieri-Neumann-Strebel-Renz invariants of the weak commutativity construction $\X(G)$
论文作者
论文摘要
对于有限生成的组$ g $，我们计算了Bieri-neumann-strebel-renz不变$σ^1（\ x（g））$，用于弱通勤构建$ \ x（g）$。用$ s（\ x（g）/ w（g））$识别$ s（\ x（g））$，我们显示$σ^2（\ x（g），\ z）\ subseteqσ^2（\ x（g）/ w（g）/ w（g），\ z），\ z），\ z）$ and and $σ^2（g）$σ^2（\ x（g））当$ w（g）$有限地生成时，是平等性，我们明确计算$σ^2（g）/ w（g），\ z）$和$σ^2（\ x（g）/ w（g）/ w（g））$。我们完全计算了组$ν（g）$的维度1和2的$σ$ invariants，并表明，如果$ g $有限地生成具有有限的换向器子组，那么非亚洲张量Square $ g \ otimes G $有限地呈现。
For a finitely generated group $G$ we calculate the Bieri-Neumann-Strebel-Renz invariant $Σ^1(\X(G))$ for the weak commutativity construction $\X(G)$. Identifying $S(\X(G))$ with $S(\X(G) / W(G))$ we show $Σ^2(\X(G),\Z) \subseteq Σ^2(\X(G)/ W(G),\Z)$ and $Σ^2(\X(G)) \subseteq $ $ Σ^2(\X(G)/ W(G))$ that are equalities when $W(G)$ is finitely generated and we explicitly calculate $Σ^2(\X(G)/ W(G),\Z)$ and $ Σ^2(\X(G)/ W(G))$ in terms of the $Σ$-invariants of $G$. We calculate completely the $Σ$-invariants in dimensions 1 and 2 of the group $ν(G)$ 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.
