English

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