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Journal Article

Free subgroups of 3-manifold groups

MPS-Authors
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Belolipetsky,  Mikhail
Max Planck Institute for Mathematics, Max Planck Society;

External Ressource

https://doi.org/10.4171/GGD/542
(Publisher version)

Fulltext (public)

arXiv:1803.05868.pdf
(Preprint), 186KB

Supplementary Material (public)
There is no public supplementary material available
Citation

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


Cite as: http://hdl.handle.net/21.11116/0000-0006-D82F-3
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.