Ahmad Issa (University of Texas at Austin)
Non-geometric veering triangulations
In 2010 Ian Agol introduced a class of "veering" ideal triangulations for mapping tori of pseudo-Anosov homeomorphisms of surfaces punctured along the singular points of the invariant foliations. These triangulations have very special combinatorial properties, and Agol asked if these are "geometric", i.e. realised in the complete hyperbolic metric with all tetrahedra positively oriented. In this talk I'll describe Agol's elegant construction of these triangulations using train tracks on surfaces, and give the first examples of non-geometric veering triangulations.