Journal of Lie Theory
8(1), 1-23 (1998)

A geometric study of Fibonacci groups

H. Helling, A. C. Kim, J. L. Mennicke

Fakultät für Mathematik
Universität Bielefeld
Postfach 10 01 31
D--33501 Bielefeld

Department of Mathematics
Pusan National University

Abstract: Fibonacci groups are recovered as fundamental groups of certain closed hyperbolic $\scriptstyle3$-manifolds. This is achieved by constructing compact hyperbolic polyhedra in dimension $\scriptstyle3$ which are fundamental domains of torsion free lattices in $\scriptstyle {\rm SL}_2(\mathbb{C})$. Their presentation can be read off by classical methods. This presentation can easily be given standard Fibonacci form.

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