Patrick Nairne

Obstructions to embeddings between trees

We will detail a new obstruction to the existence of rough isometric embeddings between certain metric trees. By passing to the boundary, this will also provide obstructions to bilipschitz embeddings between certain metric Cantor sets. The obstruction will be the unboundedness of an intriguing integer sequence (the "build-up sequence") that you can naturally associate to a pair of spherically homogeneous metric trees. At the end, we will discuss applications to the quasiisometric rigidity of Baumslag-Solitar groups.