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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

DOI: 10.2140/gt.2011.15.2073

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

Mathematical Subject Classification

Primary: 57M50

References
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/