Solvable Baumslag-Solitar Lattices

Noah Caplinger

paper

Solvable Baumslag-Solitar Lattices

arXiv:2408.13381

Abstract

The solvable Baumslag Solitar groups $BS (1, n)$ each admit a canonical model space, $X_{n}$ . We give a complete classification of lattices in $G_{n} = Isom^{+} (X_{n})$ and find that such lattices fail to be strongly rigid$\unicode{x2014}$there are automorphisms of lattices $I^ \subset G_{n}$ which do not extend to $G_{n}$ $\unicode{x2014}$but do satisfy a weaker form of rigidity: for all isomorphic lattices $I^_{1}, I^_{2} \subset G_{n}$ , there is an automorphism $I ¨ \in Aut (G_{n})$ so that $I ¨ (I^_{1}) = I^_{2}$ .