Geometry, Topology and Dynamics Seminar
Nathan Dunfield
UIUC
Increasing the number of fibered faces of arithmetic hyperbolic 3-manifolds
Abstract: I will exhibit a closed hyperbolic 3-manifold which
satisfies a very strong form of Thurston's Virtual Fibration
Conjecture. In particular, this manifold has finite covers which
fiber over the circle in arbitrarily many fundamentally distinct
ways. More precisely, it has a tower of finite covers where the
number of fibered faces of the Thurston norm ball goes to infinity, in
fact faster than any power of the logarithm of the degree of the
cover. The example manifold $M$ is arithmetic, and the proof uses
detailed number-theoretic information, at the level of the Hecke
eigenvalues, to drive a geometric argument based on Fried's dynamical
characterization of the fibered faces. The origin of the basic
fibration of $M$ over the circle is the modular elliptic curve
$E=X_0(49)$, which admits multiplication by the ring of integers of
$\mathbb Q[\sqrt{-7}]$. This is joint work with Dinakar Ramakrishnan.
Monday November 24, 2008 at 3:00 PM in SEO 612