Volume 18, issue 2 (2018)

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Taut branched surfaces from veering triangulations

Michael Landry

Algebraic & Geometric Topology 18 (2018) 1089–1114
Abstract

Let $M$ be a closed hyperbolic $3$–manifold with a fibered face $\sigma$ of the unit ball of the Thurston norm on ${H}_{2}\left(M\right)$. If $M$ satisfies a certain condition related to Agol’s veering triangulations, we construct a taut branched surface in $M$ spanning $\sigma$. This partially answers a 1986 question of Oertel, and extends an earlier partial answer due to Mosher.

Keywords
branched surface, Thurston norm, veering triangulation
Primary: 57M99
Publication
Received: 2 May 2017
Revised: 21 September 2017
Accepted: 30 September 2017
Published: 12 March 2018
Authors
 Michael Landry Mathematics Department Yale University New Haven, CT United States