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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Subgroup distortion of 3-manifold groups


Authors: Hoang Thanh Nguyen and Hongbin Sun
Journal: Trans. Amer. Math. Soc. 373 (2020), 6683-6711
MSC (2010): Primary 20F65, 20F67, 57M50
DOI: https://doi.org/10.1090/tran/8139
Published electronically: July 3, 2020
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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.


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Additional Information

Hoang Thanh Nguyen
Affiliation: Beijing International Center for Mathematical Research, Peking University, Beijing 100871, People’s Republic of China
MR Author ID: 1310129
Email: htnguyen.dn.vn@outlook.com

Hongbin Sun
Affiliation: Department of Mathematics, Rutgers University-New Brunswick, Hill center, Busch Campus, Piscataway, New Jersey 08854
MR Author ID: 898463
Email: hongbin.sun@rutgers.edu

DOI: https://doi.org/10.1090/tran/8139
Received by editor(s): October 22, 2019
Received by editor(s) in revised form: February 9, 2020, and February 10, 2020
Published electronically: July 3, 2020
Additional Notes: The second author was partially supported by NSF grant DMS-1840696.
Article copyright: © Copyright 2020 American Mathematical Society