Generalised Fibonacci manifolds (Q1377354)

Fibonacci manifolds \(M_n\) are compact orientable 3-manifolds whose fundamental groups are the Fibonacci groups \(F_{2n}\) \((=F_{2,2n})\). These manifolds have a hyperbolic structure which may be defined via Fibonacci numbers. In the present paper, 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 is examined.