An introduction to veering triangulations
Saul Schleimer (Warwick)
Abstract: Singular euclidean structures on surfaces are a key tool in
the study of the mapping class group, of Teichmüller space, and of
kleinian three-manifolds. François Guéritaud, while studying work of
Ian Agol, gave a powerful technique for turning a singular euclidean
structure (on a surface) into a triangulation (of a three-manifold).
We will give an exposition of some of this work from the point of view
of Delaunay triangulations for the L^\infty metric. We will review
the definitions in a relaxed fashion, discuss the technique, and then
present applications to the study of strata in the space of singular
euclidean structures. If time permits, we will also discuss the
naturally occurring algorithmic questions.
This is joint work with Mark Bell and Vaibhav Gadre. Some of our
results are independently due to Ian Frankel, who has different
applications.