Profinite Graphs and Groups

TL;DR: The right-angled Artin pro-$p$ group associated to a simplicial graph was shown to be a Bloch-Kato group in this paper, and the Smoothness Conjecture of De Clercq and Florens holds for this group.

TL;DR: The right-angled Artin pro-p$p$ group GΓ$G_{\Gamma }$ associated to a finite simplicial graph Γ$Gamma$ was shown to be a right-angle Artin group in this paper .

TL;DR: In this article, it was shown that a pair of mapping classes are said to be procongruent if they induce a conjugate pair of outer automophisms on the profinite completion of the fundamental group of the surface.

TL;DR: In this article, a class of profinite groups defined via extensions of centralizers analogous to the extensively studied class of finitely generated fully residually free groups, that is, limit groups (in the sense of Z. Sela), is introduced and investigated.