A pro-$p$ version of Sela’s accessibility and Poincaré duality pro-$p$ groups

Abstract

We prove a pro-$p$ version of Sela’s theorem (1997) stating that a finitely generated group is $k$-acylindrically accessible. This result is then used to prove that ${\mathrm{PD}}^n$ pro-$p$ groups admit a unique $k$-acylindrical JSJ-decomposition.