Free subgroups of 3-manifold groups

@article{Belolipetsky2018FreeSO,
  title={Free subgroups of 3-manifold groups},
  author={M. Belolipetsky and Cayo D'oria},
  journal={arXiv: Group Theory},
  year={2018}
}
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… Expand
1 Citations
Sequences of high rank lattices with large systole containing a fixed genus surface group .
In this paper we exhibit sequences of torsion-free lattices (both uniform and non-uniform) that have arbitrary large systole, but all containing a thin surface subgroup of fixed genus.

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