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Fractional Fibonacci groups and manifolds. (English. Russian original) Zbl 0917.20032

Sib. Math. J. 39, No. 4, 655-664 (1998); translation from Sib. Mat. Zh. 39, No. 4, 765-775 (1998).
The authors introduce fractional Fibonacci groups which generalize the classical Fibonacci groups as well as their generalization introduced by C. Maclachlan. In the article under review, this generalization is studied and justified from the topological point of view.
The authors study in detail three-dimensional manifolds whose fundamental groups are fractional Fibonacci groups. In particular, hyperbolic manifolds among them are distinguished and various constructions of such manifolds are described as branched coverings of the three-sphere.

MSC:

20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
57M05 Fundamental group, presentations, free differential calculus
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57N10 Topology of general \(3\)-manifolds (MSC2010)
20F05 Generators, relations, and presentations of groups

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