Explicit angle structures for veering triangulations

Futer, David¹ ; Guéritaud, François²

¹Department of Mathematics, Temple University, Philadelphia, PA 19122, USA
²Laboratoire Paul Painlevé, CNRS UMR 8524, Université de Lille 1, 59650 Villeneuve d’Ascq, France

Algebraic and Geometric Topology, Tome 13 (2013) no. 1, pp. 205-235

Résumé

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.

Détail

DOI : 10.2140/agt.2013.13.205

Keywords: veering triangulation, angle structure, geometric structure, hyperbolic surface bundle

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