A note on covers of fibred hyperbolic manifolds

2016/02/18 by Jérôme Los, Los, Jérôme, Luisa Paoluzzi +3
Mathematics · #37E30 #57M10 #57M50 #57M60 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:37E30 #msc:57M10 #msc:57M50 #msc:57M60

paper · pdf · doi:10.48550/arxiv.1602.05776

9 pages, 2 figures

arxiv created 2016/02/18 · arxiv updated 2016/02/19

Abstract

For each surface S of genus g>2 we construct pairs of conjugate pseudo-Anosov maps, φ₁ and φ₂, and two non-equivalent covers p_i: S \longrightarrow S, i=1,2, so that the lift of φ₁ to S with respect to p₁ coincides with that of φ₂ with respect to p₂. The mapping tori of the φ_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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