Seminars & Colloquia Calendar

Download as iCal file

Topology/Geometry Seminar

Thurston's norm, veering triangulations, and a new polynomial invariant

Michael Landry (WUSTL)

Location:  zoom link:
Date & time: Tuesday, 17 November 2020 at 3:50PM - 4:50PM

I will describe two related papers concerning the Thurston norm on homology. This norm is a 3-manifold invariant with connections to many areas: geometric group theory, foliation theory, Floer theory, and more. There are some beautiful clues due to Thurston, Fried, Mosher, McMullen, and others that indicate there should be a dictionary between the combinatorics of the norm's polyhedral unit ball and the geometric/topological structures existing in the underlying manifold. However, this picture is incomplete and is mostly limited to the case when the manifold is a surface bundle over the circle. I will explain some results which go beyond the surface bundle case to the more general setting of manifolds admitting veering triangulations, which are combinatorial objects I will define. First I will explain that one of these objects always cuts out the cone over a face of the norm ball in a natural way and computes the norm in this cone. Second, I will explain how one can use these objects to collate all surfaces representing classes in these cones which are compact leaves of taut foliations. Third, I will describe joint work with Yair Minsky and Samuel Taylor in which we use a veering triangulation to define a polynomial invariant, the "veering polynomial," generalizing the Teichmuller polynomial of McMullen and answering a question asked by Calegari and McMullen. This invariant can be obtained by computing the Perron polynomial of a certain directed graph.

Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.