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Generalised Fibonacci manifolds

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Abstract

Fibonacci manifolds have a hyperbolic structure which may be defined via Fibonacci numbers. Using related sequences of Lucas numbers, other 3-manifolds are constructed, their geometric structures determined, and a curious relationship between the homology and the invariant trace-field examined.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Aberdeen, AB24 3QY, Aberdeen, UK

    C. Maclachlan

  2. Department of Mathematics, University of Texas, 78712, Austin, TX, USA

    A. W. Reid

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  1. C. Maclachlan
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  2. A. W. Reid
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Supported by the Royal Society.

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Maclachlan, C., Reid, A.W. Generalised Fibonacci manifolds. Transformation Groups 2, 165–182 (1997). https://doi.org/10.1007/BF01235939

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