Algebraic & Geometric Topology

Explicit angle structures for veering triangulations

David Futer and François Guéritaud

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715496

Digital Object Identifier
doi:10.2140/agt.2013.13.205

Mathematical Reviews number (MathSciNet)
MR3031641

Zentralblatt MATH identifier
1270.57054

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

Keywords
veering triangulation angle structure geometric structure hyperbolic surface bundle

Citation

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. https://projecteuclid.org/euclid.agt/1513715496


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References

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