# Taut branched surfaces from veering triangulations

## TL;DR

This paper constructs taut branched surfaces in hyperbolic 3-manifolds with fibered faces, using veering triangulations, partially answering a longstanding question and extending previous work.

## Contribution

It introduces a method to build taut branched surfaces from veering triangulations in certain hyperbolic 3-manifolds, addressing a question from 1985.

## Key findings

- Constructed taut branched surfaces spanning fibered faces
- Extended previous partial results by Mosher
- Provided new insights into the structure of hyperbolic 3-manifolds

## Abstract

Let $M$ be a closed hyperbolic 3-manifold with a fibered face $\sigma$ of the unit ball of the Thurston norm on $H_2(M)$. 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 1985 question of Oertel, and extends an earlier partial answer due to Mosher.