Finding fibre faces in finite covers
type: Item
instance of: scholarly article
title: Finding fibre faces in finite covers
zbMATH Open document ID: 1148.57003
published in: Mathematical Research Letters
publication date: 2008-08-12T00:00:00Z
review text: In this beautiful note the authors prove the following result and corollary: Theorem: Let \(M\) be a closed arithmetic hyperbolic \(3\)-manifold which fibres over the circle. Then given any \(K \in \mathbb{N}\), there exists a finite sheeted covering of \(M\) for which the unit ball of Thurston norm has more than \(K\) fibred faces. Corollary: Let \(M\) be a closed arithmetic hyperbolic \(3\)-manifold which fibres over the circle. Then the rank of the second homology can be increased without bound. The proof of the theorem is purely geometric; the authors apply standard arguments for flows and make use of the arithmeticity of \(M \cong \mathbb{H}^3 / \Gamma\), particularly of the fact that the commensurator of \(\Gamma\) in \(PSL(2,\mathbb{C})\) is dense.
Mathematics Subject Classification ID: 57M10
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 51M10
zbMATH DE Number: 5310651
zbMATH Keywords: arithmetic hyperbolic 3-manifold
zbMATH Keywords: Betti number
zbMATH Keywords: second homology
zbMATH Keywords: finite cover
author: D. D. Long
author: Alan W. Reid
MaRDI profile type: Publication
full work available at URL: mrl.2008.v15.n3.a11
OpenAlex ID: W2094193252
DOI: 10.4310/MRL.2008.V15.N3.A11
description: scientific article; zbMATH DE number 5310651