Solvable Baumslag-Solitar Lattices
Abstract
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 $\Gamma \subset G_n$ which do not extend to $G_n$$\unicode{x2014}$but do satisfy a weaker form of rigidity: for all isomorphic lattices $\Gamma_1,\Gamma_2\subset G_n$, there is an automorphism $\rho \in \text{Aut}(G_n)$ so that $\rho(\Gamma_1) = \Gamma_2$.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.13381
- arXiv:
- arXiv:2408.13381
- Bibcode:
- 2024arXiv240813381C
- Keywords:
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- Mathematics - Group Theory