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Description

Pseudo-Anosov flows are a class of dynamical systems on three-manifolds with deep connections to the topology and geometry of their underlying spaces. For instance, features of the flow are closely related to the manifold’s hyperbolic geometry, embedded surfaces, and fundamental group. A modern approach to studying these flows is with veering triangulations. These are rigid combinatorial objects that have provided new computational and algorithmic techniques to study the flows. In this talk, I will first give a broad overview of the correspondence between these flows and triangulations. I will then discuss my work on more flexible triangulations that capture a larger class of pseudo-Anosov flows and yield new explicit examples.