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arXiv · 2110.14834

The BNS invariants of the generalized solvable Baumslag-Solitar groups and of their finite index subgroups

Wagner Sgobbi·Peter Wong
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Abstract

We compute the Bieri-Neumann-Strebel invariants $\Sigma^1$ for the generalized solvable Baumslag-Solitar groups $\Gamma_n$ and their finite index subgroups. Using $\Sigma^1$, we show that certain finite index subgroups of $\Gamma_n$ cannot be isomorphic to $\Gamma_{k}$ for any $k$. In addition, we use the BNS-invariants to give a new proof of property $R_\infty$ for the groups $\Gamma_n$ and their finite index subgroups.

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Wagner Sgobbi, Peter Wong. 2021-10-28. The BNS invariants of the generalized solvable Baumslag-Solitar groups and of their finite index subgroups. https://arxiv.org/abs/2110.14834

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