Anna Parlak

Pseudo-Anosov flows and twisted Alexander polynomials

The Teichmüller polynomial is an invariant associated to a fibered face of the Thurston norm ball of a hyperbolic 3-manifold. Its main feature is that it packages information about the stretch factors of monodromies of all fibrations lying over that face.

Recently Landry-Minsky-Taylor used veering triangulations to define a new invariant, called the taut polynomial. It can be associated to any pseudo-Anosov flow without perfect fits, and generalizes the Teichmüller polynomial to the non-fibered setting.

I will explain why the taut polynomial is always just a certain twisted Alexander polynomial of the underlying manifold, and discuss some consequences of this result.