Pushing fillings in right-angled Artin groups

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

doi:10.1112/jlms/jds064

Pushing fillings in right-angled Artin groups

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

Mathematics

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

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 r^2k+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 language	English (US)
Pages (from-to)	663-688
Number of pages	26
Journal	Journal of the London Mathematical Society
Volume	87
Issue number	3
DOIs	https://doi.org/10.1112/jlms/jds064
State	Published - Jun 2013

ASJC Scopus subject areas

General Mathematics

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10.1112/jlms/jds064

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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",

note = "Funding Information: This work was supported by a SQuaRE grant from the American Institute of Mathematics. The second author and the fourth author were partially supported by NSF grants DMS-0906962 and DMS-0906086, respectively. The third author was partially supported by the Louisiana Board of Regents Support Fund contract LEQSF(2011-14)-RD-A-06. The fifth author would like to thank New York University for its hospitality during the preparation of this paper.",

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doi = "10.1112/jlms/jds064",

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T1 - Pushing fillings in right-angled Artin groups

AU - Abrams, Aaron

AU - Brady, Noel

AU - Dani, Pallavi

AU - Duchin, Moon

AU - Young, Robert

N1 - Funding Information: This work was supported by a SQuaRE grant from the American Institute of Mathematics. The second author and the fourth author were partially supported by NSF grants DMS-0906962 and DMS-0906086, respectively. The third author was partially supported by the Louisiana Board of Regents Support Fund contract LEQSF(2011-14)-RD-A-06. The fifth author would like to thank New York University for its hospitality during the preparation of this paper.

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.

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JF - Journal of the London Mathematical Society

IS - 3

ER -

Pushing fillings in right-angled Artin groups

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