A note on covers of fibred hyperbolic manifolds
Résumé
For each surface S of genus g > 2 we construct pairs of conjugate pseudo-Anosov maps, phi(1) and phi(2), and two non-equivalent covers p(j): (S) over tilde -> S i = 1,2, so that the lift of phi(1) to (S) over tilde with respect to p(1) coincides with one of phi(2) with respect to p(2).
The mapping tori of the phi(i) and their lift provide examples of pairs of hyperbolic 3-manifolds so that the fi rst is covered by the second in two different ways.