Special subgroups of Bianchi groups

  • Michelle Chu

    The University of Texas at Austin, USA
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We determine C-special subgroups of the Bianchi groups with index bounded above by 120 by effectivising the arguments of Agol-Long-Reid. These subgroups are congruence of level 2 or 4 and retract to the free group on two generators. As a consequence, we find a C-special 20-sheeted cover of the figure-eight knot complement. We also determine C-special congruence subgroups for a family of cocompact arithmetic Kleinian groups.

Cite this article

Michelle Chu, Special subgroups of Bianchi groups. Groups Geom. Dyn. 14 (2020), no. 1, pp. 41–59

DOI 10.4171/GGD/533