Abstract
For each surface $S$ of genus $g>2$ we construct pairs of conjugate pseudo-Anosov maps, $\varphi_1$ and $\varphi_2$, and two non-equivalent covers $p_i\colon \tilde S \longrightarrow S$, $i=1,2$, so that the lift of $\varphi_1$ to~$\tilde S$ with respect to $p_1$ coincides with one of $\varphi_2$ with respect to $p_2$.
The mapping tori of the $\varphi_i$ and their lift provide examples of pairs of hyperbolic $3$-manifolds so that the first is covered by the second in two different ways.
Citation
Jérôme Los. Luisa Paoluzzi. António Salgueiro. "A Note on Covers of Fibred Hyperbolic Manifolds." Publ. Mat. 61 (2) 517 - 527, 2017. https://doi.org/10.5565/PUBLMAT6121707
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