Maximal ranks of free abelian subgroups of generalized cactus groups associated with finite Coxeter systems
Year: 2026
Type: preprint
Abstract: We determine the maximum ranks of free abelian subgroups of generalized cactus groups associated with finite Coxeter systems. To obtain the upper bounds, we use the cubical flat torus theorem of Wise and Woodhouse. We then verify the sharpness of these upper bounds by constructing free abelian subgroups of the corresponding ranks. Our result shows that the maximal ranks of free abelian subgroups of ordinary cactus groups can be larger than conjectured by Genevois. As an application, we show that these groups are not quasi-isometric to any right-angled Artin group unless they are virtually free abelian.
Source: arXiv (Cornell University)
Authors: Kim, Jan, Kim, Junseok
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G6312077453
OpenAlex ID: W7223095239