Volume 13, issue 1 (2013)

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Explicit angle structures for veering triangulations

David Futer and François Guéritaud

Algebraic & Geometric Topology 13 (2013) 205–235
Abstract

Agol recently introduced the notion of a veering triangulation, and showed that such triangulations naturally arise as layered triangulations of fibered hyperbolic 3–manifolds. We prove, by a constructive argument, that every veering triangulation admits positive angle structures, recovering a result of Hodgson, Rubinstein, Segerman, and Tillmann. Our construction leads to explicit lower bounds on the smallest angle in this positive angle structure, and to information about angled holonomy of the boundary tori.

Keywords
veering triangulation, angle structure, geometric structure, hyperbolic surface bundle
Mathematical Subject Classification 2000
Primary: 57M50, 57R05
References
Publication
Received: 13 January 2011
Revised: 29 May 2012
Accepted: 18 August 2012
Published: 14 February 2013
Authors
David Futer
Department of Mathematics
Temple University
Philadelphia, PA 19122
USA
François Guéritaud
Laboratoire Paul Painlevé
CNRS UMR 8524
Université de Lille 1
59650 Villeneuve d’Ascq
France