Special subgroups of Bianchi groups

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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.

Original languageEnglish (US)
Pages (from-to)41-59
Number of pages19
JournalGroups, Geometry, and Dynamics
Issue number1
StatePublished - 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© European Mathematical Society


  • Coxeter groups
  • Hyperbolic 3-manifolds
  • Kleinian groups
  • Virtually special groups


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