Open Access
2017 A Note on Covers of Fibred Hyperbolic Manifolds
Jérôme Los, Luisa Paoluzzi, António Salgueiro
Publ. Mat. 61(2): 517-527 (2017). DOI: 10.5565/PUBLMAT6121707


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.


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Jérôme Los. Luisa Paoluzzi. António Salgueiro. "A Note on Covers of Fibred Hyperbolic Manifolds." Publ. Mat. 61 (2) 517 - 527, 2017.


Received: 2 December 2015; Revised: 23 January 2017; Published: 2017
First available in Project Euclid: 29 June 2017

zbMATH: 1380.57017
MathSciNet: MR3677870
Digital Object Identifier: 10.5565/PUBLMAT6121707

Primary: 57M10
Secondary: 37E30 , 57M50 , 57M60

Keywords: (Pseudo-)Anosov diffeomorphisms , Mapping tori , Regular covers

Rights: Copyright © 2017 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.61 • No. 2 • 2017
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