Explicit angle structures for veering triangulations

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.

23 pages, 8 figures. v2 contains a cleaner definition of holonomy in Section 6.1, and minor expository changes throughout. To appear in Algebraic & Geometric Topology

References in corpus (6)

• On canonical triangulations of once-punctured torus bundles and two-bridge link complements
• Taut ideal triangulations of 3-manifolds
• Angled decompositions of arborescent link complements
• Veering triangulations admit strict angle structures
• Ideal triangulations of 3-manifolds II: taut and angle structures
• An algorithm to determine the Heegaard genus of simple 3-manifolds with non-empty boundary

Cited by in corpus (10)

• Veering triangulations and Cannon-Thurston maps
• Taut branched surfaces from veering triangulations
• Dynamics of veering triangulations: infinitesimal components of their flow graphs and applications
• The taut polynomial and the Alexander polynomial
• Geometric triangulations and highly twisted links
• Constructing Birkhoff sections for pseudo-Anosov flows with controlled complexity
• Experimental statistics of veering triangulations
• A survey of hyperbolic knot theory
• Geometric triangulations of a family of hyperbolic 3-braids
• Mutations and faces of the Thurston norm ball dynamically represented by multiple distinct flows