#### 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