Random groups at density $d<3/14$ act non-trivially on a CAT(0) cube complex
Group Theory
2022-08-26 v2
Abstract
For random groups in the Gromov density model at , we construct walls in the Cayley complex which give rise to a non-trivial action by isometries on a CAT(0) cube complex. This extends results of Ollivier-Wise and Mackay-Przytycki at densities and , respectively. We are able to overcome one of the main combinatorial challenges remaining from the work of Mackay-Przytycki, and we give a construction that plausibly works at any density .
Keywords
Cite
@article{arxiv.2106.14931,
title = {Random groups at density $d<3/14$ act non-trivially on a CAT(0) cube complex},
author = {MurphyKate Montee},
journal= {arXiv preprint arXiv:2106.14931},
year = {2022}
}
Comments
30 pages, 17 figures Several revisions to exposition made based on reviewer comments. Replaced Definition 4.6 with Definition 4.6 and Construction 4.7. Accepted version, to appear in Transactions of the AMS