English

Random Group Actions on $\mathrm{CAT}(0)$ Square Complexes

Group Theory 2022-10-13 v1

Abstract

We generalize ideas of Jahncke from trees to square complexes. We introduce the notion of progression in CAT(0)\mathrm{CAT}(0) square complexes. Using progression, we are able to build on the proof strategy of Dahmani-Guirardel-Przytycki to show any action of a random group with seven or more generators on a CAT(0)\mathrm{CAT}(0) square complex has a global fixed point.

Keywords

Cite

@article{arxiv.2210.06378,
  title  = {Random Group Actions on $\mathrm{CAT}(0)$ Square Complexes},
  author = {Zachary Munro},
  journal= {arXiv preprint arXiv:2210.06378},
  year   = {2022}
}

Comments

15 pages

R2 v1 2026-06-28T03:27:57.910Z