Algebra/Topology Seminar

Speaker: Anna Parlak

Title: Veering triangulations, the Teichmüller polynomial and the Alexander polynomial

Abstract: Veering triangulations are a special class of ideal triangulations with a rather mysterious combinatorial definition. Their importance follows from a deep connection with pseudo-Anosov flows on 3-manifolds. Recently Landry, Minsky and Taylor introduced a polynomial invariant of veering triangulations called the taut polynomial. It is a generalisation of an older invariant, the Teichmüller polynomial, defined by McMullen in 2002. 

The aim of my talk is to demonstrate that veering triangulations provide a convenient setup for computations. More precisely, I will use fairly easy arguments to obtain a  fairly strong statement which generalises the results of McMullen relating the Teichmüller polynomial to the Alexander polynomial.  

No prior knowledge on the Alexander polynomial, the Teichmüller polynomial or veering triangulations  will be assumed.