Solvable Baumslag-Solitar Lattices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917757535125504 |
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| author | Caplinger, Noah |
| author_facet | Caplinger, Noah |
| contents | The solvable Baumslag Solitar groups $\text{BS}(1,n)$ each admit a canonical model space, $X_n$. We give a complete classification of lattices in $G_n = \text{Isom}^+(X_n)$ and find that such lattices fail to be strongly rigid$\unicode{x2014}$there are automorphisms of lattices $Γ\subset G_n$ which do not extend to $G_n$$\unicode{x2014}$but do satisfy a weaker form of rigidity: for all isomorphic lattices $Γ_1,Γ_2\subset G_n$, there is an automorphism $ρ\in \text{Aut}(G_n)$ so that $ρ(Γ_1) = Γ_2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_13381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solvable Baumslag-Solitar Lattices Caplinger, Noah Group Theory The solvable Baumslag Solitar groups $\text{BS}(1,n)$ each admit a canonical model space, $X_n$. We give a complete classification of lattices in $G_n = \text{Isom}^+(X_n)$ and find that such lattices fail to be strongly rigid$\unicode{x2014}$there are automorphisms of lattices $Γ\subset G_n$ which do not extend to $G_n$$\unicode{x2014}$but do satisfy a weaker form of rigidity: for all isomorphic lattices $Γ_1,Γ_2\subset G_n$, there is an automorphism $ρ\in \text{Aut}(G_n)$ so that $ρ(Γ_1) = Γ_2$. |
| title | Solvable Baumslag-Solitar Lattices |
| topic | Group Theory |
| url | https://arxiv.org/abs/2408.13381 |