Explicit angle structures for veering triangulations

Futer, David; Guéritaud, François

doi:10.2140/agt.2013.13.205

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Explicit angle structures for veering triangulations

David Futer and François Guéritaud

Algebraic & Geometric Topology 13 (2013) 205–235

DOI: 10.2140/agt.2013.13.205

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

Volume 13, issue 1 (2013)