Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic finite type groups, to FC-type We show that class is closed under intersection. also study an analog curve complex mapping group constructed by Cumplido et al. using subgroups. extend construction this complex, called subgroups...

We prove that any large even Artin group is poly-free and based on a triangle graph also poly-free.

González-Acuña showed that Artin presentations characterize closed, orientable 3-manifold groups. Winkelnkemper later discovered each presentation determines a smooth, compact, simply connected 4-manifold. We utilize triangle groups to find all on two generators present the trivial group. then determine 4-manifolds with second betti number at most appear in theory.

Let A L $A_L$ be the right-angled Artin group associated with a finite flag complex $L$ . We show that amenable category of equals virtual cohomological dimension Coxeter W $W_L$ In particular, groups satisfy question Capovilla–Löh–Moraschini proposing an inequality between and Farber's topological complexity.