researchseminars.org

Michael Landry (WUSTL)
2020-07-21 15:00 - 15:30 UTC | https://researchseminars.org/talk/GaTO/19/
Title: Faces of the Thurston norm ball up to isotopy (https://researchseminars.org/talk/GaTO/19/)
by Michael Landry (WUSTL) as part of Geometry and topology online

Abstract

Let \(M\) be a three-manifold with
nondegenerate Thurston norm \(x\) on its second homology.
There is a partial dictionary between the combinatorics
of the polyhedral unit ball of \(x\) and
the topological features of \(M\). This dictionary is
quite incomplete, but its existing entries are tantalizing.

Currently, most of the entries of this dictionary concern
fibered faces of the unit ball. Thurston proved that these
organize all fibrations of \(M\) over the circle. Fried and
Mosher tell us more: for each fibered face \(F\) there is a
(canonical) pseudo-Anosov flow whose Euler class computes the
norm \(x\) in the cone over \(F\). Furthermore, the flow
"sees" certain least-complexity surfaces. Further work of
Mosher shows that, under certain conditions, pseudo-Anosov
flows can naturally specify nonfibered faces of the unit ball.

After giving some of this background I will discuss results
from my recent preprint (see link). I
show that Agol's veering triangulations can be used to
determine faces of Thurston norm balls, to compute the
Thurston norm over those faces, and to collate all isotopy
classes of least-complexity surfaces over those faces. This
analysis includes nonfibered faces.

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