Divergence and quasi-isometry classes of random Gromov's monsters
Group Theory
2018-05-11 v1
Abstract
We show that Gromov's monsters arising from i.i.d. random labellings of expanders (that we call random Gromov's monsters) have linear divergence along a subsequence, so that in particular they do not contain Morse quasigeodesics, and they are not quasi-isometric to Gromov's monsters arising from graphical small cancellation labellings of expanders. Moreover, by further studying the divergence function, we show that there are uncountably many quasi-isometry classes of random Gromov's monsters.
Keywords
Cite
@article{arxiv.1805.04039,
title = {Divergence and quasi-isometry classes of random Gromov's monsters},
author = {Dominik Gruber and Alessandro Sisto},
journal= {arXiv preprint arXiv:1805.04039},
year = {2018}
}
Comments
17 pages, 1 figure