Subgroup distortion of 3-manifold groups

Nguyen, Hoang; Sun, Hongbin

doi:10.1090/tran/8139

Subgroup distortion of 3-manifold groups
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by Hoang Thanh Nguyen and Hongbin Sun PDF

Trans. Amer. Math. Soc. 373 (2020), 6683-6711 Request permission

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.

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