Upper and lower train track

Description

For a given Transverse veering triangulation, we define the upper and lower train track. These are train tracks drawn on the upper- or underside of the tetrahedrons. They are interesting because they form as Train track splitting sequence when taking horizontal slices through the veering triangulation. These train tracks will later form the skeleton of the Upper and lower branched surface

Definition

Let $\mathcal{V}$ be a Transverse veering triangulation. Let $f$ be a face of the triangulation. This face has an assigned upper and lower side. Let $t$ and $t^{\prime }$ be the tetrahedra above and below. The upper train track ${\tau }^f$ consists of two branches drawn on $f$ meeting in a cusp. Edges start from the midpoints of the equatorial edges of $t$ and meet at the midpoint of the non-equitorial edge of $t$. Similarly, the lower train track the two branches of ${\tau }_f$ start at the equatorial edges of $t^{\prime }$ and meet at the non-equatorial edge of $t^{\prime }$.

Properties

Ich habe das in in dem Paper lit_schleimerVeeringTriangulationsDynamic2023 gelesen.