Free subgroups of 3-manifold groups

  • Mikhail Belolipetsky

    IMPA - Instituto Nacional de Matematica Pura e Aplicada, Rio de Janeiro, Brazil
  • Cayo Dória

    IMPA - Instituto Nacional de Matematica Pura e Aplicada, Rio de Janeiro, Brazil
Free subgroups of 3-manifold groups cover

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Abstract

We show that any closed hyperbolic 3-manifold has a co-final tower of covers of degrees such that any subgroup of generated by elements is free, where and . Together with this result we prove that , where denotes the systole of , thus providing a large set of new examples for a conjecture of Gromov. In the second theorem is an absolute constant. We also consider a generalization of these results to non-compact finite volume hyperbolic 3-manifolds.

Cite this article

Mikhail Belolipetsky, Cayo Dória, Free subgroups of 3-manifold groups. Groups Geom. Dyn. 14 (2020), no. 1, pp. 243–254

DOI 10.4171/GGD/542