Uniqueness theorem for completely non-degenerate B-groups

doi:10.4213/im9714e

Uniqueness theorem for completely non-degenerate B-groups

2026-01-01

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Alexey Glutsyuk *

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Yulij Sergeevich Ilyashenko

DOI：10.4213/im9714e

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We show that a completely non-degenerate B-group is uniquely determined by its factor: two such groups with conformally equivalent factors are Mo & uml;bius conjugate. A similar property is inherent to the quasi-Fuchsian groups but not to degenerate B-groups. We also study the factor of a B-group as a triple: the main factor, the marked characteristic complex, and a homotopy class of maps of the first to the second one.

Keywords:

Kleinian groups

non-degenerate B-groups

factor complex

Uniqueness theorem for completely non-degenerate B-groups

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