Hyperbolic manifolds fibering over the circle
Geb 20.30, SR 2.058
Abstract: A celebrated theorem by Agol and Wise states that every hyperbolic 3-manifold virtually fibers over the circle. This is someway surprising, as whenever a hyperbolic manifold fibers, its fibers can never be embedded in a nice way. While the situation in dimension 3 is understood, the same can not be said of higher dimensions, as even producing a single example of a high-dimensional hyperbolic manifold which fibers over the circle is a challenging task. After reviewing the state of the art in dimension 3, we will introduce some combinatorial tools, inspired by a work of Jankiewicz, Norin, and Wise, that can be used to construct a hyperbolic 5-manifold which fibers over the circle. This is joint work with Giovanni Italiano and Bruno Martelli.