- Series
- Geometry Topology Seminar
- Time
- Monday, February 24, 2020 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Henry Segerman – Oklahoma State University – segerman@math.okstate.edu
- Organizer
- Dan Margalit
Agol introduced veering triangulations of mapping tori, whose combinatorics are canonically associated to the pseudo-Anosov monodromy. In unpublished work, Guéritaud and Agol generalise an alternative construction to any closed manifold equipped with a pseudo-Anosov flow without perfect fits.
Schleimer and I build the reverse map. As a first step, we construct the link space for a given veering triangulation. This is a copy of
R2, equipped with transverse stable and unstable foliations, from which the Agol-Guéritaud's construction recovers the veering
triangulation. The link space is analogous to Fenley's orbit space for a pseudo-Anosov flow.
Along the way, we construct a canonical circular ordering of the cusps of the universal cover of a veering triangulation. I will also talk about work with Giannopolous and Schleimer building a census of transverse veering triangulations. The current census lists all transverse veering triangulations with up to 16 tetrahedra, of which there are 87,047.