Résume | Problems of quasiisometric rigidity in geometric group theory ask the following: If finitely generated groups G and H are quasiisometric (i.e. they are metrically similar) then do they have to be algebraically similar (e.g. commensurable)?
In this talk we will study the above question, but under the weaker assumption that there only exists a quasiisometric embedding of G into H. We will answer it in the case when G and H are solvable Baumslag-Solitar groups, generalising work of Farb and Mosher. The problem reduces to understanding embeddings between regular rooted trees which in turn reduces to understanding the properties of an interesting and novel integer sequence. |