Geometry, Topology and Dynamics Seminar
Nathan Dunfield
UIUC
A tale of two norms
Abstract: The first cohomology of a hyperbolic 3-manifold has two natural norms:
the Thurston norm, which measures the topological complexity of surfaces
representing the dual homology class, and the harmonic norm, which is
just the $L^2$ norm on the corresponding space of harmonic 1-forms.
Bergeron-Sengun-Venkatesh recently showed that these two norms are
closely related, at least when the injectivity radius is bounded below.
Their work was motivated by the connection of the harmonic norm to the
Ray-Singer analytic torsion and issues of torsion growth. After carefully
introducing both norms and the connection to torsion growth, I will discuss
new results that refine and clarify the precise relationship between them;
one tool here will be a third norm based on least-area surfaces. This is
joint work with Jeff Brock.
Monday February 22, 2016 at 3:00 PM in SEO 636