Volume 15, issue 4 (2011)

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Veering triangulations admit strict angle structures

Craig D Hodgson, J Hyam Rubinstein, Henry Segerman and Stephan Tillmann

Geometry & Topology 15 (2011) 2073–2089
Abstract

Agol recently introduced the concept of a veering taut triangulation of a $3$–manifold, which is a taut ideal triangulation with some extra combinatorial structure. We define the weaker notion of a “veering triangulation” and use it to show that all veering triangulations admit strict angle structures. We also answer a question of Agol, giving an example of a veering taut triangulation that is not layered.

Keywords
veering triangulation, angle structure, geometric structure, hyperbolic surface bundle
Primary: 57M50
Publication
Received: 30 November 2010
Revised: 17 June 2011
Accepted: 19 September 2011
Published: 23 October 2011
Proposed: David Gabai
Seconded: Joan Birman, Colin Rourke
Authors
 Craig D Hodgson Department of Mathematics and Statistics The University of Melbourne Melbourne Parkville VIC 3010 Australia http://www.ms.unimelb.edu.au/~cdh/ J Hyam Rubinstein Department of Mathematics and Statistics The University of Melbourne Melbourne Parkville VIC 3010 Australia http://www.ms.unimelb.edu.au/~rubin/ Henry Segerman Department of Mathematics and Statistics The University of Melbourne Melbourne Parkville VIC 3010 Australia http://www.ms.unimelb.edu.au/~segerman/ Stephan Tillmann School of Mathematics and Physics The University of Queensland Brisbane QLD 4072 Australia http://www.maths.uq.edu.au/~tillmann/