Residually free groups do not admit a uniform polynomial isoperimetric function

Claudio Llosa Isenrich; Romain Tessera

doi:10.1090/proc/15082

Residually free groups do not admit a uniform polynomial isoperimetric function

Claudio Llosa Isenrich, Romain Tessera

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

Abstract

We show that there is no uniform polynomial isoperimetric function for finitely presented subgroups of direct products of free groups by producing a sequence of subgroups G_r ≤ F₂⁽¹⁾ × ··· × F₂⁽r⁾ of direct products of 2-generated free groups with Dehn functions bounded below by n^r. The groups G_r are obtained from the examples of non-coabelian subdirect products of free groups constructed by Bridson, Howie, Miller, and Short. As a consequence we obtain that residually free groups do not admit a uniform polynomial isoperimetric function.

Original language	English
Pages (from-to)	4203-4212
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	10
DOIs	https://doi.org/10.1090/proc/15082
Publication status	Published - 1 Oct 2020
Externally published	Yes

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title = "Residually free groups do not admit a uniform polynomial isoperimetric function",

abstract = "We show that there is no uniform polynomial isoperimetric function for finitely presented subgroups of direct products of free groups by producing a sequence of subgroups Gr ≤ F2(1) × ··· × F2(r) of direct products of 2-generated free groups with Dehn functions bounded below by nr. The groups Gr are obtained from the examples of non-coabelian subdirect products of free groups constructed by Bridson, Howie, Miller, and Short. As a consequence we obtain that residually free groups do not admit a uniform polynomial isoperimetric function.",

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AU - Tessera, Romain

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N2 - We show that there is no uniform polynomial isoperimetric function for finitely presented subgroups of direct products of free groups by producing a sequence of subgroups Gr ≤ F2(1) × ··· × F2(r) of direct products of 2-generated free groups with Dehn functions bounded below by nr. The groups Gr are obtained from the examples of non-coabelian subdirect products of free groups constructed by Bridson, Howie, Miller, and Short. As a consequence we obtain that residually free groups do not admit a uniform polynomial isoperimetric function.

AB - We show that there is no uniform polynomial isoperimetric function for finitely presented subgroups of direct products of free groups by producing a sequence of subgroups Gr ≤ F2(1) × ··· × F2(r) of direct products of 2-generated free groups with Dehn functions bounded below by nr. The groups Gr are obtained from the examples of non-coabelian subdirect products of free groups constructed by Bridson, Howie, Miller, and Short. As a consequence we obtain that residually free groups do not admit a uniform polynomial isoperimetric function.

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SP - 4203

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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Residually free groups do not admit a uniform polynomial isoperimetric function

Abstract

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