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Fractional Fibonacci groups with an odd number of generators

Chinyere, Ihechukwu and Williams, Gerald (2022) 'Fractional Fibonacci groups with an odd number of generators.' Topology and its Applications, 312. p. 108083. ISSN 0016-660X

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Abstract

The Fibonacci groups F (n) are known to exhibit significantly different behaviour depending on the parity of n. We extend known results for F (n) for odd n to the family of Fractional Fibonacci groups F k/l(n). We show that for odd n the group F k/l(n) is not the fundamental group of an orientable hyperbolic 3-orbifold of finite volume. We obtain results concerning the existence of torsion in the groups F k/l(n) (where n is odd) paying particular attention to the groups F k(n) and F k/l(3), and observe consequences concerning the asphericity of relative presentations of their shift extensions. We show that if F k(n) (where n is odd) and F k/l(3) are non-cyclic 3-manifold groups then they are isomorphic to the direct product of the quaternion group Q₈ and a finite cyclic group.

Item Type: Article
Additional Information: 17 pages
Uncontrolled Keywords: Fibonacci group; Cyclically presented group; Orbifold; Manifold; Aspherical presentation
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 04 Apr 2022 13:57
Last Modified: 25 May 2022 16:41
URI: http://repository.essex.ac.uk/id/eprint/32676

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