We introduce a family of conditions on a simplicial complex that we call local k-largeness
(k≥ 6 is an integer). They are simply stated, combinatorial and easily checkable. One of our …

Any diagram group over a finite semigroup presentation acts properly, freely, and cellularly
by isometrices on a proper CAT (0) cubical complex. The existence of a proper, cellular …

A Tits alternative theorem is proved in this paper for groups acting on CAT (0) cubical
complexes. That is, a proof is given to show that if G is assumed to be a group for which …

For a two-dimensional Artin group whose associated Coxeter group is hyperbolic, we prove
that the action of on the hyperbolic space obtained by coning off certain subcomplexes of its …

Let be an orientable surface of finite type and let Mod (Σ) be its mapping class group. We
consider actions of Mod () by semisimple isometries on complete CAT (0) spaces. If the …

Tits Alternative for 2-dimensional CAT(0) complexes Page 1 Forum of Mathematics, Pi (2022),
Vol. 10:e25 1–19 doi:10.1017/fmp.2022.20 RESEARCH ARTICLE Tits Alternative for 2-dimensional …

We show that two-dimensional Artin groups satisfy a strengthening of the Tits alternative:
their subgroups either contain a non-abelian free group or are virtually free abelian of rank …

Given an Artin group A Γ, a common strategy in the study of A Γ is the reduction to parabolic
subgroups whose defining graphs have small diameter, ie, showing that A Γ has a specific …

Cocompactly cubulated 2-dimensional Artin groups Page 1 Comment. Math. Helv. 91 (2016),
519–542 DOI 10.4171/CMH/394 Commentarii Mathematici Helvetici © Swiss Mathematical …

We investigate the cocompact action of Higman's group on a CAT (0) square complex
associated to its standard presentation. We show that this action is in a sense intrinsic, which …