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Free subgroups of 3-manifold groups

Belolipetsky, M., & Dória, C. (2020). Free subgroups of 3-manifold groups. Groups, Geometry, and Dynamics, 14(1), 243-254. doi:10.4171/GGD/542.

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Genre: Journal Article
Latex : Free subgroups of $3$-manifold groups

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arXiv:1803.05868.pdf (Preprint), 186KB
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Belolipetsky-Doria_Free subgroups of 3-manifold groups_2020.pdf (Publisher version), 179KB

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https://doi.org/10.4171/GGD/542 (Publisher version)
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Creators:
Belolipetsky, Mikhail1, Author
Dória, Cayo, Author
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201

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Free keywords: Mathematics, Group Theory, Geometric Topology
Abstract: We show that any closed hyperbolic $3$-manifold $M$ has a co-final tower of covers $M_i \to M$ of degrees $n_i$ such that any subgroup of $\pi_1(M_i)$ generated by $k_i$ elements is free, where $k_i \ge n_i^C$ and $C = C(M) > 0$. Together with this result we show that $\log k_i \geq C_1 sys_1(M_i)$, where $sys_1(M_i)$ denotes the systole of $M_i$, thus providing a large set of new examples for a conjecture of Gromov. In the second theorem $C_1> 0$ is an absolute constant. We also consider a generalization of these results to non-compact finite volume hyperbolic $3$-manifolds.

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Language(s): eng - English
Dates: 2020
Publication Status: Published in print
Pages: 12
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Rev. Type: Peer
Degree: -

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### Source 1

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Title: Groups, Geometry, and Dynamics
Abbreviation : Groups Geom. Dyn.
Source Genre: Journal
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Publ. Info: European Mathematical Society
Pages: - Volume / Issue: 14 (1) Sequence Number: - Start / End Page: 243 - 254 Identifier: -