Fibred and Virtually Fibred Hyperbolic 3-Manifolds in the Censuses

Abstract

Continuing the work of Dunfield, we determine the fibred status of all the unknown hyperbolic 3-manifolds in the cusped census. We then find all the fibred hyperbolic 3-manifolds in the closed census and use this to find over 100 examples each of closed and cusped nonfibred virtually fibred census 3-manifolds, including the Weeks manifold. We also show that the corank of the fundamental group of every 3-manifold in the cusped and in the closed census is 0 or 1.

Keywords:

• Primary 57N10, 57M05
• Fibred
• 3-manifolds
• census