The profinite completion of accessible groups

Abstract

We introduce a class \({\mathcal {A}}\) of finitely generated residually finite accessible groups with a certain natural restriction on one-ended vertex groups in their JSJ-decompositions. We prove that the profinite completion of groups in \({\mathcal {A}}\) almost detects its JSJ-decomposition and compute the genus of free products of groups in \({\mathcal {A}}\).