Subgroup distortion of 3-manifold groups

Hoang Thanh Nguyen; Hongbin Sun

doi:10.1090/tran/8139

Subgroup distortion of 3-manifold groups

Hoang Thanh Nguyen, Hongbin Sun

School of Arts and Sciences, Mathematics

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

Abstract

In this paper, we compute the subgroup distortion of all finitely generated subgroups of all finitely generated 3-manifold groups, and the subgroup distortion in this case can only be linear, quadratic, exponential and double exponential. It turns out that the subgroup distortion of a subgroup of a 3-manifold group is closely related to the separability of this subgroup.

Original language	English (US)
Pages (from-to)	6683-6711
Number of pages	29
Journal	Transactions of the American Mathematical Society
Volume	373
Issue number	9
DOIs	https://doi.org/10.1090/tran/8139
State	Published - Sep 2020

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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abstract = "In this paper, we compute the subgroup distortion of all finitely generated subgroups of all finitely generated 3-manifold groups, and the subgroup distortion in this case can only be linear, quadratic, exponential and double exponential. It turns out that the subgroup distortion of a subgroup of a 3-manifold group is closely related to the separability of this subgroup.",

author = "Nguyen, {Hoang Thanh} and Hongbin Sun",

note = "Funding Information: Received by the editors October 22, 2019, and, in revised form, February 9, 2020, and February 10, 2020. 2010 Mathematics Subject Classification. Primary 20F65, 20F67, 57M50. The second author was partially supported by NSF grant DMS-1840696. Publisher Copyright: {\textcopyright} 2020 American Mathematical Society",

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N2 - In this paper, we compute the subgroup distortion of all finitely generated subgroups of all finitely generated 3-manifold groups, and the subgroup distortion in this case can only be linear, quadratic, exponential and double exponential. It turns out that the subgroup distortion of a subgroup of a 3-manifold group is closely related to the separability of this subgroup.

AB - In this paper, we compute the subgroup distortion of all finitely generated subgroups of all finitely generated 3-manifold groups, and the subgroup distortion in this case can only be linear, quadratic, exponential and double exponential. It turns out that the subgroup distortion of a subgroup of a 3-manifold group is closely related to the separability of this subgroup.

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Subgroup distortion of 3-manifold groups

Abstract

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