Algebraic & Geometric Topology

Explicit angle structures for veering triangulations

David Futer and François Guéritaud

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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.

Article information

Algebr. Geom. Topol., Volume 13, Number 1 (2013), 205-235.

Received: 13 January 2011
Revised: 29 May 2012
Accepted: 18 August 2012
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds 57R05: Triangulating

veering triangulation angle structure geometric structure hyperbolic surface bundle


Futer, David; Guéritaud, François. Explicit angle structures for veering triangulations. Algebr. Geom. Topol. 13 (2013), no. 1, 205--235. doi:10.2140/agt.2013.13.205.

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