Solvable Baumslag-Solitar Lattices
Noah Caplinger · arXiv (Cornell University) · 2024
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 $ρ(Γ_1) = Γ_2$.