Divergence and quasi-isometry classes of random Gromov's monsters

Dominik Gruber; Alessandro Sisto

doi:10.1017/S0305004120000201

Divergence and quasi-isometry classes of random Gromov's monsters

Dominik Gruber
, Alessandro Sisto

Research output: Contribution to journal › Article › peer-review

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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.

Original language	English
Pages (from-to)	249-264
Number of pages	16
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	171
Issue number	2
Early online date	18 Feb 2021
DOIs	https://doi.org/10.1017/S0305004120000201
Publication status	Published - Sept 2021

Keywords

2020 Mathematics Subject Classification:
20F65

ASJC Scopus subject areas

General Mathematics

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AB - 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.

KW - 2020 Mathematics Subject Classification:

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ER -

Divergence and quasi-isometry classes of random Gromov's monsters

Abstract

Keywords

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