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

1 Citation (Scopus)

54 Downloads (Pure)

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

Access to Document

10.1017/S0305004120000201

Download pdf
© Cambridge Philosophical Society 2021
Accepted author manuscript, 407 KBLicence: CC BY-NC-ND

Cite this

@article{2a714bad62e84d1b9b95088d92d5ba77,

title = "Divergence and quasi-isometry classes of random Gromov's monsters",

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 = "2020 Mathematics Subject Classification:, 20F65",

author = "Dominik Gruber and Alessandro Sisto",

year = "2021",

month = sep,

doi = "10.1017/S0305004120000201",

language = "English",

volume = "171",

pages = "249--264",

journal = "Mathematical Proceedings of the Cambridge Philosophical Society",

issn = "0305-0041",

publisher = "Cambridge University Press",

number = "2",

}

TY - JOUR

T1 - Divergence and quasi-isometry classes of random Gromov's monsters

AU - Gruber, Dominik

AU - Sisto, Alessandro

PY - 2021/9

Y1 - 2021/9

N2 - 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.

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:

KW - 20F65

UR - http://www.scopus.com/inward/record.url?scp=85101208242&partnerID=8YFLogxK

U2 - 10.1017/S0305004120000201

DO - 10.1017/S0305004120000201

M3 - Article

AN - SCOPUS:85101208242

SN - 0305-0041

VL - 171

SP - 249

EP - 264

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this