Pushing fillings in right-angled Artin groups

Aaron Abrams, Noel Brady, Pallavi Dani, Moon Duchin, Robert Young

Research output: Contribution to journalArticle

Abstract

We obtain bounds on the higher divergence functions of right-angled Artin groups (RAAGs), finding that the k-dimensional divergence of a RAAG is bounded above by r2k+2. These divergence functions, previously defined for Hadamard manifolds to measure isoperimetric properties at infinity, are defined here as a family of quasi-isometry invariants of groups. We also show that the kth order Dehn function of a Bestvina-Brady group is bounded above by V (2k+2)/k and construct a class of RAAGs called orthoplex groups which show that each of these upper bounds is sharp.

Original languageEnglish (US)
Pages (from-to)663-688
Number of pages26
JournalJournal of the London Mathematical Society
Volume87
Issue number3
DOIs
StatePublished - Jun 2013

Fingerprint

Right-angled Artin Group
Divergence
Dehn Function
Hadamard Manifolds
Quasi-isometry
Isoperimetric
Infinity
Upper bound
Invariant

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Pushing fillings in right-angled Artin groups. / Abrams, Aaron; Brady, Noel; Dani, Pallavi; Duchin, Moon; Young, Robert.

In: Journal of the London Mathematical Society, Vol. 87, No. 3, 06.2013, p. 663-688.

Research output: Contribution to journalArticle

Abrams, Aaron ; Brady, Noel ; Dani, Pallavi ; Duchin, Moon ; Young, Robert. / Pushing fillings in right-angled Artin groups. In: Journal of the London Mathematical Society. 2013 ; Vol. 87, No. 3. pp. 663-688.
@article{dcc1b502b4ee4e88a3d784b312fe7094,
title = "Pushing fillings in right-angled Artin groups",
abstract = "We obtain bounds on the higher divergence functions of right-angled Artin groups (RAAGs), finding that the k-dimensional divergence of a RAAG is bounded above by r2k+2. These divergence functions, previously defined for Hadamard manifolds to measure isoperimetric properties at infinity, are defined here as a family of quasi-isometry invariants of groups. We also show that the kth order Dehn function of a Bestvina-Brady group is bounded above by V (2k+2)/k and construct a class of RAAGs called orthoplex groups which show that each of these upper bounds is sharp.",
author = "Aaron Abrams and Noel Brady and Pallavi Dani and Moon Duchin and Robert Young",
year = "2013",
month = "6",
doi = "10.1112/jlms/jds064",
language = "English (US)",
volume = "87",
pages = "663--688",
journal = "Journal of the London Mathematical Society",
issn = "0024-6107",
publisher = "Oxford University Press",
number = "3",

}

TY - JOUR

T1 - Pushing fillings in right-angled Artin groups

AU - Abrams, Aaron

AU - Brady, Noel

AU - Dani, Pallavi

AU - Duchin, Moon

AU - Young, Robert

PY - 2013/6

Y1 - 2013/6

N2 - We obtain bounds on the higher divergence functions of right-angled Artin groups (RAAGs), finding that the k-dimensional divergence of a RAAG is bounded above by r2k+2. These divergence functions, previously defined for Hadamard manifolds to measure isoperimetric properties at infinity, are defined here as a family of quasi-isometry invariants of groups. We also show that the kth order Dehn function of a Bestvina-Brady group is bounded above by V (2k+2)/k and construct a class of RAAGs called orthoplex groups which show that each of these upper bounds is sharp.

AB - We obtain bounds on the higher divergence functions of right-angled Artin groups (RAAGs), finding that the k-dimensional divergence of a RAAG is bounded above by r2k+2. These divergence functions, previously defined for Hadamard manifolds to measure isoperimetric properties at infinity, are defined here as a family of quasi-isometry invariants of groups. We also show that the kth order Dehn function of a Bestvina-Brady group is bounded above by V (2k+2)/k and construct a class of RAAGs called orthoplex groups which show that each of these upper bounds is sharp.

UR - http://www.scopus.com/inward/record.url?scp=84879227408&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879227408&partnerID=8YFLogxK

U2 - 10.1112/jlms/jds064

DO - 10.1112/jlms/jds064

M3 - Article

VL - 87

SP - 663

EP - 688

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 3

ER -