📝 SummarXiv

Abstract

We prove a product theorem for sublinear bilipschitz equivalences which generalizes the classical work of Kapovich, Kleiner and Leeb on quasiisometries between product spaces. We employ our product theorem to distinguish up to quasiisometry certain families among these groups which share the same dimension, cone-dimension and Dehn function; actually we do this by distinguishing them up to sublinear bilipschitz equivalence, which is slightly stronger. Especially, we recover the fact, recently obtained by Bourdon and R\'emy with different groups, that there exists uncountably many quasiisometry classes of indecomposable, non-unimodular, higher rank solvable Lie groups.