Geometry and Topology Seminar
It is now known that every closed, hyperbolic 3-manifold has a finite cover which fibers over the circle. There has been recent interest in generalizing this result in various directions. In a geometric direction, one can ask whether higher odd dimensional hyperbolic manifolds virtually fiber. In an algebraic direction one can ask which groups have algebraic analogues of a virtual fibering. In all of this, there is a curious dearth of odd-dimensional examples which do not virtually fiber. We partially correct this by constructing closed, aspherical, odd-dimensional manifolds with word hyperbolic fundamental group that do not virtually fiber over the circle. This is joint work with Grigori Avramidi and Boris Okun.