English

Virtually fibering random right-angled Coxeter groups

Combinatorics 2017-03-06 v1

Abstract

We show that the Right-Angled Coxeter group C=C(G)C=C(G) associated to a random graph GG(n,p)G\sim \mathcal{G}(n,p) with logn+loglogn+ω(1)np<1ω(n2)\frac{\log n + \log\log n + \omega(1)}{n} \leq p < 1- \omega(n^{-2}) virtually algebraically fibers. This means that CC has a finite index subgroup CC' and a finitely generated normal subgroup NCN\subset C' such that C/NZC'/N \cong \mathbb{Z}. We also obtain the corresponding hitting time statements, more precisely, we show that as soon as GG has minimum degree at least 2 and as long as it is not the complete graph, then C(G)C(G) virtually algebraically fibers. The result builds upon the work of Jankiewicz, Norin, and Wise and it is essentially best possible.

Keywords

Cite

@article{arxiv.1703.01207,
  title  = {Virtually fibering random right-angled Coxeter groups},
  author = {Gonzalo Fiz Pontiveros and Roman Glebov and Ilan Karpas},
  journal= {arXiv preprint arXiv:1703.01207},
  year   = {2017}
}
R2 v1 2026-06-22T18:34:53.270Z