Fibered faces, veering triangulations, and the arc complex

TL;DR

This paper explores the relationship between subsurface projections in curve and arc complexes and Agol's veering triangulation in fibered 3-manifolds, revealing a uniform correspondence between large-distance subsurfaces and large simplicial regions.

Contribution

It establishes a new uniform correspondence between large subsurface projections and simplicial regions in veering triangulations across all fibers in a fibered face.

Findings

Large-distance subsurfaces correspond to large simplicial regions in veering triangulations.

The correspondence is uniform across all fibers in a given fibered face.

Provides new insights into the structure of fibered 3-manifolds and their triangulations.

Abstract

We study the connections between subsurface projections in curve and arc complexes in fibered 3-manifolds and Agol's veering triangulation. The main theme is that large-distance subsurfaces in fibers are associated to large simplicial regions in the veering triangulation, and this correspondence holds uniformly for all fibers in a given fibered face of the Thurston norm.