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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:A tale of two norms. - Nathan Dunfield\, UIUC
DTSTART;TZID=Europe/London:20170208T160000
DTEND;TZID=Europe/London:20170208T170000
UID:TALK69186AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/69186
DESCRIPTION:The first cohomology of a hyperbolic 3-manifold ha
s two natural norms: the Thurston norm\, which mea
sure topological complexity of surfaces representi
ng 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-Venka
tesh recently showed that these two norms are clos
ely related\, at least when the injectivity radius
is bounded below.\n\nTheir work was motivated by
the connection of the harmonic norm to the Ray-Sin
ger analytic torsion and issues of torsion growth.
After carefully introducing both norms and the c
onnection to torsion growth\, I will discuss new r
esults that refine and clarify the precise relatio
nship between them\; one tool here will be a third
norm based on least-area surfaces. This is joint
work with Jeff Brock.
LOCATION:MR13
CONTACT:Ivan Smith
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