Australian Geometric Topology Webinar: Henry Segerman -- From veering triangulations to link spaces and back again

Inaugural Talk: Wednesday 6 May 2020, 12:00 AEST 

Henry Segerman (Oklahoma State University) 

Title: From veering triangulations to link spaces and back again 

Abstract: 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  In unpublished work,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 R^2, equipped with transverse stable
and unstable foliations, from which the Agol-Guéritaud 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.  

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